<p>Classifique em verdadeiro (V) ou falso (F):</p>
<p>a) Quaisquer que sejam os pontos <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.743ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 750.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title” data-mathml="undefined">
<title> A , B ∈ r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-41” d=“M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z”/>
<path stroke-width=“1” id=“E1-MJMAIN-2C” d=“M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z”/>
<path stroke-width=“1” id=“E1-MJMATHI-42” d=“M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z”/>
<path stroke-width=“1” id=“E1-MJMAIN-2208” d=“M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z”/>
<path stroke-width=“1” id=“E1-MJMATHI-72” d=“M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z”/>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-41" x=“0” y=“0”/>
<use xlink:href="#E1-MJMAIN-2C" x=“750” y=“0”/>
<use xlink:href="#E1-MJMATHI-42" x=“1195” y=“0”/>
<use xlink:href="#E1-MJMAIN-2208" x=“2232” y=“0”/>
<use xlink:href="#E1-MJMATHI-72" x=“3178” y=“0”/>
</g>
</svg>.</p>
<p>a) Quaisquer que sejam os pontos <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.743ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 750.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title” data-mathml="undefined">
<title> A , B ∈ r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-41” d=“M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z”/>
<path stroke-width=“1” id=“E1-MJMAIN-2C” d=“M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z”/>
<path stroke-width=“1” id=“E1-MJMATHI-42” d=“M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z”/>
<path stroke-width=“1” id=“E1-MJMAIN-2208” d=“M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z”/>
<path stroke-width=“1” id=“E1-MJMATHI-72” d=“M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z”/>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-41" x=“0” y=“0”/>
<use xlink:href="#E1-MJMAIN-2C" x=“750” y=“0”/>
<use xlink:href="#E1-MJMATHI-42" x=“1195” y=“0”/>
<use xlink:href="#E1-MJMAIN-2208" x=“2232” y=“0”/>
<use xlink:href="#E1-MJMATHI-72" x=“3178” y=“0”/>
</g>
</svg>.</p>
Passo 1
<p>Olá! Vamos analisar essas afirmações de geometria.</p>
<p>Temos quatro sentenças para classificar como verdadeiras (V) ou falsas (F), baseadas nos axiomas e propriedades básicas da geometria euclidiana plana.</p>
<p><b>Como vamos resolver isso?</b></p>
<p>Vamos analisar cada afirmação separadamente, usando os postulados fundamentais da geometria:</p>
<ul>
<li>Por dois pontos distintos passa uma única reta.</li>
<li>Por um ponto passam infinitas retas.</li>
<li>Uma reta é um conjunto infinito de pontos.</li>
<li>Se dois pontos coincidem, a noção de “reta que passa por eles” é a mesma que “reta que passa por um ponto” (infinitas retas).</li>
</ul>
<p>Vamos verificar cada caso.</p>
<p>Temos quatro sentenças para classificar como verdadeiras (V) ou falsas (F), baseadas nos axiomas e propriedades básicas da geometria euclidiana plana.</p>
<p><b>Como vamos resolver isso?</b></p>
<p>Vamos analisar cada afirmação separadamente, usando os postulados fundamentais da geometria:</p>
<ul>
<li>Por dois pontos distintos passa uma única reta.</li>
<li>Por um ponto passam infinitas retas.</li>
<li>Uma reta é um conjunto infinito de pontos.</li>
<li>Se dois pontos coincidem, a noção de “reta que passa por eles” é a mesma que “reta que passa por um ponto” (infinitas retas).</li>
</ul>
<p>Vamos verificar cada caso.</p>
Passo 2
<p><b>a) Quaisquer que sejam os pontos </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.019ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 869.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.013ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 866.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-42" x=“0” y=“0”></use>
</g>
</svg><b>, se </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.019ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 869.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
</g>
</svg><b> é distinto de </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.013ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 866.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-42" x=“0” y=“0”></use>
</g>
</svg><b>, então existe uma reta a tal que </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.332ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 2726.1 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A ∈ a</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2208” d=“M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-61” d=“M222 -8Q140 -8 89 34T38 158Q38 191 48 227Q72 329 151 390T327 452Q361 452 385 443T421 425T433 416H434L441 421Q448 426 460 430T486 435Q509 435 523 422T538 386Q538 380 522 315T488 179T467 93Q466 87 466 72Q466 42 483 42Q505 42 521 75Q531 94 541 134Q546 155 550 158T571 162H576H587Q607 162 607 148Q606 142 604 132T590 94T566 47T528 9T474 -8Q396 -8 358 40Q295 -8 222 -8ZM404 351Q383 401 324 401Q300 401 270 385T221 330Q206 296 186 220Q166 136 166 106Q166 72 184 58T228 43Q256 43 284 57T328 84T343 103Q343 106 374 228L404 351Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2208" x=“1147” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-61" x=“2092” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.325ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 2723.1 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B ∈ a</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2208” d=“M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-61” d=“M222 -8Q140 -8 89 34T38 158Q38 191 48 227Q72 329 151 390T327 452Q361 452 385 443T421 425T433 416H434L441 421Q448 426 460 430T486 435Q509 435 523 422T538 386Q538 380 522 315T488 179T467 93Q466 87 466 72Q466 42 483 42Q505 42 521 75Q531 94 541 134Q546 155 550 158T571 162H576H587Q607 162 607 148Q606 142 604 132T590 94T566 47T528 9T474 -8Q396 -8 358 40Q295 -8 222 -8ZM404 351Q383 401 324 401Q300 401 270 385T221 330Q206 296 186 220Q166 136 166 106Q166 72 184 58T228 43Q256 43 284 57T328 84T343 103Q343 106 374 228L404 351Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-42" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2208" x=“1144” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-61" x=“2089” y=“0”></use>
</g>
</svg><b>.</b></p>
<p>Essa é a própria definição do primeiro postulado da geometria: por dois pontos distintos sempre passa uma reta.</p>
<p>E, de fato, existe (é a reta que os contém). Portanto, é <b>verdadeiro</b>.</p>
<p>Beleza?</p>
<title> A</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.013ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 866.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-42" x=“0” y=“0”></use>
</g>
</svg><b>, se </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.019ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 869.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
</g>
</svg><b> é distinto de </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.013ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 866.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-42" x=“0” y=“0”></use>
</g>
</svg><b>, então existe uma reta a tal que </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.332ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 2726.1 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A ∈ a</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2208” d=“M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-61” d=“M222 -8Q140 -8 89 34T38 158Q38 191 48 227Q72 329 151 390T327 452Q361 452 385 443T421 425T433 416H434L441 421Q448 426 460 430T486 435Q509 435 523 422T538 386Q538 380 522 315T488 179T467 93Q466 87 466 72Q466 42 483 42Q505 42 521 75Q531 94 541 134Q546 155 550 158T571 162H576H587Q607 162 607 148Q606 142 604 132T590 94T566 47T528 9T474 -8Q396 -8 358 40Q295 -8 222 -8ZM404 351Q383 401 324 401Q300 401 270 385T221 330Q206 296 186 220Q166 136 166 106Q166 72 184 58T228 43Q256 43 284 57T328 84T343 103Q343 106 374 228L404 351Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2208" x=“1147” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-61" x=“2092” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.325ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 2723.1 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B ∈ a</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2208” d=“M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-61” d=“M222 -8Q140 -8 89 34T38 158Q38 191 48 227Q72 329 151 390T327 452Q361 452 385 443T421 425T433 416H434L441 421Q448 426 460 430T486 435Q509 435 523 422T538 386Q538 380 522 315T488 179T467 93Q466 87 466 72Q466 42 483 42Q505 42 521 75Q531 94 541 134Q546 155 550 158T571 162H576H587Q607 162 607 148Q606 142 604 132T590 94T566 47T528 9T474 -8Q396 -8 358 40Q295 -8 222 -8ZM404 351Q383 401 324 401Q300 401 270 385T221 330Q206 296 186 220Q166 136 166 106Q166 72 184 58T228 43Q256 43 284 57T328 84T343 103Q343 106 374 228L404 351Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-42" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2208" x=“1144” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-61" x=“2089” y=“0”></use>
</g>
</svg><b>.</b></p>
<p>Essa é a própria definição do primeiro postulado da geometria: por dois pontos distintos sempre passa uma reta.</p>
<p>E, de fato, existe (é a reta que os contém). Portanto, é <b>verdadeiro</b>.</p>
<p>Beleza?</p>
Passo 3
<p><b>b) Quaisquer que sejam os pontos </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.968ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 847.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-50” d=“M162 62L302 623Q302 624 258 624H234Q214 624 209 626T200 638Q200 677 217 684Q220 686 439 686Q667 685 684 682Q686 681 693 680Q713 677 733 671T782 649T829 602T847 528Q847 450 784 382T604 293Q571 288 469 287H373L346 176Q340 151 333 122T321 78L317 64Q317 62 361 62H387Q420 62 420 44Q417 10 404 2L399 0L357 1Q331 2 224 2Q149 2 109 1T65 0Q43 0 43 17Q43 21 47 33Q52 54 57 58T89 62H113H162ZM692 558Q692 611 617 622Q610 623 529 624H452L381 343H458H492Q604 343 641 389Q662 414 677 471T692 558Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-50" x=“0” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.019ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 869.5 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Q</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-51” d=“M53 245Q53 297 70 356T125 478T216 590T349 671T523 703Q656 703 735 637T815 445Q815 410 808 370T781 277T729 178T643 87T519 14L525 4Q540 -19 553 -25T592 -32Q632 -32 654 -24T680 -7T689 10T704 18Q713 18 717 12T722 0Q722 -8 711 -36T681 -101T624 -166T541 -194Q513 -194 494 -183T465 -157T450 -118T444 -79T443 -41V-7L433 -9Q391 -17 344 -17Q301 -17 263 -10T185 15T118 62T71 138T53 245ZM666 482Q666 529 652 563T614 615T565 640T512 648Q412 648 335 573Q268 506 235 389T201 202Q201 164 210 136T230 95T259 66L262 76Q269 109 302 135T382 162Q401 162 415 159T449 140T484 92L491 78L496 82Q502 86 505 88T515 97T528 107T541 120T555 137T570 156T585 179T599 205T612 235Q629 278 647 351T666 482ZM439 56Q439 58 439 62T435 75T426 92T410 106T383 112Q353 112 332 96T311 63Q311 38 355 38H366Q391 39 415 45T439 56Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-51" x=“0” y=“0”></use>
</g>
</svg><b> e as retas </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.23ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 529.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-72" x=“0” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.234ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 531.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> s</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-73” d=“M140 290Q140 311 148 336T176 388T235 433T326 451H336Q355 451 373 449T418 439T460 412T476 363Q476 333 456 311T406 289Q384 289 371 302T357 335Q357 351 364 364T379 384L386 391Q386 392 381 394T362 398T330 400Q299 400 278 393T247 373T235 352T232 335Q232 322 242 312Q258 299 315 290T403 260Q457 224 457 167Q457 152 453 134T435 90T397 43T330 7T229 -8Q133 -8 95 22T57 91Q57 127 81 152T139 177Q161 177 177 164T194 121Q189 80 153 56Q179 43 236 43Q275 43 303 52T343 75T361 101T366 124Q366 148 338 161T272 180T232 186Q187 198 164 227T140 290Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-73" x=“0” y=“0”></use>
</g>
</svg><b>, se </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.968ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 847.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-50” d=“M162 62L302 623Q302 624 258 624H234Q214 624 209 626T200 638Q200 677 217 684Q220 686 439 686Q667 685 684 682Q686 681 693 680Q713 677 733 671T782 649T829 602T847 528Q847 450 784 382T604 293Q571 288 469 287H373L346 176Q340 151 333 122T321 78L317 64Q317 62 361 62H387Q420 62 420 44Q417 10 404 2L399 0L357 1Q331 2 224 2Q149 2 109 1T65 0Q43 0 43 17Q43 21 47 33Q52 54 57 58T89 62H113H162ZM692 558Q692 611 617 622Q610 623 529 624H452L381 343H458H492Q604 343 641 389Q662 414 677 471T692 558Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-50" x=“0” y=“0”></use>
</g>
</svg><b> é distinto de </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.019ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 869.5 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Q</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-51” d=“M53 245Q53 297 70 356T125 478T216 590T349 671T523 703Q656 703 735 637T815 445Q815 410 808 370T781 277T729 178T643 87T519 14L525 4Q540 -19 553 -25T592 -32Q632 -32 654 -24T680 -7T689 10T704 18Q713 18 717 12T722 0Q722 -8 711 -36T681 -101T624 -166T541 -194Q513 -194 494 -183T465 -157T450 -118T444 -79T443 -41V-7L433 -9Q391 -17 344 -17Q301 -17 263 -10T185 15T118 62T71 138T53 245ZM666 482Q666 529 652 563T614 615T565 640T512 648Q412 648 335 573Q268 506 235 389T201 202Q201 164 210 136T230 95T259 66L262 76Q269 109 302 135T382 162Q401 162 415 159T449 140T484 92L491 78L496 82Q502 86 505 88T515 97T528 107T541 120T555 137T570 156T585 179T599 205T612 235Q629 278 647 351T666 482ZM439 56Q439 58 439 62T435 75T426 92T410 106T383 112Q353 112 332 96T311 63Q311 38 355 38H366Q391 39 415 45T439 56Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-51" x=“0” y=“0”></use>
</g>
</svg><b>, e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.968ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 847.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-50” d=“M162 62L302 623Q302 624 258 624H234Q214 624 209 626T200 638Q200 677 217 684Q220 686 439 686Q667 685 684 682Q686 681 693 680Q713 677 733 671T782 649T829 602T847 528Q847 450 784 382T604 293Q571 288 469 287H373L346 176Q340 151 333 122T321 78L317 64Q317 62 361 62H387Q420 62 420 44Q417 10 404 2L399 0L357 1Q331 2 224 2Q149 2 109 1T65 0Q43 0 43 17Q43 21 47 33Q52 54 57 58T89 62H113H162ZM692 558Q692 611 617 622Q610 623 529 624H452L381 343H458H492Q604 343 641 389Q662 414 677 471T692 558Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-50" x=“0” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.019ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 869.5 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Q</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-51” d=“M53 245Q53 297 70 356T125 478T216 590T349 671T523 703Q656 703 735 637T815 445Q815 410 808 370T781 277T729 178T643 87T519 14L525 4Q540 -19 553 -25T592 -32Q632 -32 654 -24T680 -7T689 10T704 18Q713 18 717 12T722 0Q722 -8 711 -36T681 -101T624 -166T541 -194Q513 -194 494 -183T465 -157T450 -118T444 -79T443 -41V-7L433 -9Q391 -17 344 -17Q301 -17 263 -10T185 15T118 62T71 138T53 245ZM666 482Q666 529 652 563T614 615T565 640T512 648Q412 648 335 573Q268 506 235 389T201 202Q201 164 210 136T230 95T259 66L262 76Q269 109 302 135T382 162Q401 162 415 159T449 140T484 92L491 78L496 82Q502 86 505 88T515 97T528 107T541 120T555 137T570 156T585 179T599 205T612 235Q629 278 647 351T666 482ZM439 56Q439 58 439 62T435 75T426 92T410 106T383 112Q353 112 332 96T311 63Q311 38 355 38H366Q391 39 415 45T439 56Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-51" x=“0” y=“0”></use>
</g>
</svg><b> pertencem às retas </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.23ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 529.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-72" x=“0” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.234ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 531.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> s</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-73” d=“M140 290Q140 311 148 336T176 388T235 433T326 451H336Q355 451 373 449T418 439T460 412T476 363Q476 333 456 311T406 289Q384 289 371 302T357 335Q357 351 364 364T379 384L386 391Q386 392 381 394T362 398T330 400Q299 400 278 393T247 373T235 352T232 335Q232 322 242 312Q258 299 315 290T403 260Q457 224 457 167Q457 152 453 134T435 90T397 43T330 7T229 -8Q133 -8 95 22T57 91Q57 127 81 152T139 177Q161 177 177 164T194 121Q189 80 153 56Q179 43 236 43Q275 43 303 52T343 75T361 101T366 124Q366 148 338 161T272 180T232 186Q187 198 164 227T140 290Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-73" x=“0” y=“0”></use>
</g>
</svg><b>, então </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“5.563ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 2395.1 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> r = s</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-73” d=“M140 290Q140 311 148 336T176 388T235 433T326 451H336Q355 451 373 449T418 439T460 412T476 363Q476 333 456 311T406 289Q384 289 371 302T357 335Q357 351 364 364T379 384L386 391Q386 392 381 394T362 398T330 400Q299 400 278 393T247 373T235 352T232 335Q232 322 242 312Q258 299 315 290T403 260Q457 224 457 167Q457 152 453 134T435 90T397 43T330 7T229 -8Q133 -8 95 22T57 91Q57 127 81 152T139 177Q161 177 177 164T194 121Q189 80 153 56Q179 43 236 43Q275 43 303 52T343 75T361 101T366 124Q366 148 338 161T272 180T232 186Q187 198 164 227T140 290Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-72" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“807” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-73" x=“1863” y=“0”></use>
</g>
</svg><b>.</b></p>
<p>Vamos interpretar: temos dois pontos distintos <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.745ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 751.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.838ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 791.5 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Q</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-51” d=“M399 -80Q399 -47 400 -30T402 -11V-7L387 -11Q341 -22 303 -22Q208 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435Q740 255 592 107Q529 47 461 16L444 8V3Q444 2 449 -24T470 -66T516 -82Q551 -82 583 -60T625 -3Q631 11 638 11Q647 11 649 2Q649 -6 639 -34T611 -100T557 -165T481 -194Q399 -194 399 -87V-80ZM636 468Q636 523 621 564T580 625T530 655T477 665Q429 665 379 640Q277 591 215 464T153 216Q153 110 207 59Q231 38 236 38V46Q236 86 269 120T347 155Q372 155 390 144T417 114T429 82T435 55L448 64Q512 108 557 185T619 334T636 468ZM314 18Q362 18 404 39L403 49Q399 104 366 115Q354 117 347 117Q344 117 341 117T337 118Q317 118 296 98T274 52Q274 18 314 18Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-51" x=“0” y=“0”></use>
</g>
</svg>. Eles pertencem a duas retas, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.049ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 451.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-72” d=“M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-72" x=“0” y=“0”></use>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.09ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 469.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> s</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-73” d=“M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-73" x=“0” y=“0”></use>
</g>
</svg>. Isso significa que tanto <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.049ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 451.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-72” d=“M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-72" x=“0” y=“0”></use>
</g>
</svg> quanto <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.09ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 469.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> s</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-73” d=“M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-73" x=“0” y=“0”></use>
</g>
</svg> passam por <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.745ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 751.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.838ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 791.5 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Q</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-51” d=“M399 -80Q399 -47 400 -30T402 -11V-7L387 -11Q341 -22 303 -22Q208 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435Q740 255 592 107Q529 47 461 16L444 8V3Q444 2 449 -24T470 -66T516 -82Q551 -82 583 -60T625 -3Q631 11 638 11Q647 11 649 2Q649 -6 639 -34T611 -100T557 -165T481 -194Q399 -194 399 -87V-80ZM636 468Q636 523 621 564T580 625T530 655T477 665Q429 665 379 640Q277 591 215 464T153 216Q153 110 207 59Q231 38 236 38V46Q236 86 269 120T347 155Q372 155 390 144T417 114T429 82T435 55L448 64Q512 108 557 185T619 334T636 468ZM314 18Q362 18 404 39L403 49Q399 104 366 115Q354 117 347 117Q344 117 341 117T337 118Q317 118 296 98T274 52Q274 18 314 18Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-51" x=“0” y=“0”></use>
</g>
</svg>.</p>
<p>Mas o postulado diz que por dois pontos distintos passa uma única reta. Portanto, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.049ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 451.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-72” d=“M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-72" x=“0” y=“0”></use>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.09ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 469.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> s</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-73” d=“M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-73" x=“0” y=“0”></use>
</g>
</svg> devem ser a mesma reta. A afirmação é <b>verdadeira</b>.</p>
<p>Show?</p>
<title> P</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-50” d=“M162 62L302 623Q302 624 258 624H234Q214 624 209 626T200 638Q200 677 217 684Q220 686 439 686Q667 685 684 682Q686 681 693 680Q713 677 733 671T782 649T829 602T847 528Q847 450 784 382T604 293Q571 288 469 287H373L346 176Q340 151 333 122T321 78L317 64Q317 62 361 62H387Q420 62 420 44Q417 10 404 2L399 0L357 1Q331 2 224 2Q149 2 109 1T65 0Q43 0 43 17Q43 21 47 33Q52 54 57 58T89 62H113H162ZM692 558Q692 611 617 622Q610 623 529 624H452L381 343H458H492Q604 343 641 389Q662 414 677 471T692 558Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-50" x=“0” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.019ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 869.5 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Q</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-51” d=“M53 245Q53 297 70 356T125 478T216 590T349 671T523 703Q656 703 735 637T815 445Q815 410 808 370T781 277T729 178T643 87T519 14L525 4Q540 -19 553 -25T592 -32Q632 -32 654 -24T680 -7T689 10T704 18Q713 18 717 12T722 0Q722 -8 711 -36T681 -101T624 -166T541 -194Q513 -194 494 -183T465 -157T450 -118T444 -79T443 -41V-7L433 -9Q391 -17 344 -17Q301 -17 263 -10T185 15T118 62T71 138T53 245ZM666 482Q666 529 652 563T614 615T565 640T512 648Q412 648 335 573Q268 506 235 389T201 202Q201 164 210 136T230 95T259 66L262 76Q269 109 302 135T382 162Q401 162 415 159T449 140T484 92L491 78L496 82Q502 86 505 88T515 97T528 107T541 120T555 137T570 156T585 179T599 205T612 235Q629 278 647 351T666 482ZM439 56Q439 58 439 62T435 75T426 92T410 106T383 112Q353 112 332 96T311 63Q311 38 355 38H366Q391 39 415 45T439 56Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-51" x=“0” y=“0”></use>
</g>
</svg><b> e as retas </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.23ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 529.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-72" x=“0” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.234ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 531.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> s</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-73” d=“M140 290Q140 311 148 336T176 388T235 433T326 451H336Q355 451 373 449T418 439T460 412T476 363Q476 333 456 311T406 289Q384 289 371 302T357 335Q357 351 364 364T379 384L386 391Q386 392 381 394T362 398T330 400Q299 400 278 393T247 373T235 352T232 335Q232 322 242 312Q258 299 315 290T403 260Q457 224 457 167Q457 152 453 134T435 90T397 43T330 7T229 -8Q133 -8 95 22T57 91Q57 127 81 152T139 177Q161 177 177 164T194 121Q189 80 153 56Q179 43 236 43Q275 43 303 52T343 75T361 101T366 124Q366 148 338 161T272 180T232 186Q187 198 164 227T140 290Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-73" x=“0” y=“0”></use>
</g>
</svg><b>, se </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.968ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 847.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-50” d=“M162 62L302 623Q302 624 258 624H234Q214 624 209 626T200 638Q200 677 217 684Q220 686 439 686Q667 685 684 682Q686 681 693 680Q713 677 733 671T782 649T829 602T847 528Q847 450 784 382T604 293Q571 288 469 287H373L346 176Q340 151 333 122T321 78L317 64Q317 62 361 62H387Q420 62 420 44Q417 10 404 2L399 0L357 1Q331 2 224 2Q149 2 109 1T65 0Q43 0 43 17Q43 21 47 33Q52 54 57 58T89 62H113H162ZM692 558Q692 611 617 622Q610 623 529 624H452L381 343H458H492Q604 343 641 389Q662 414 677 471T692 558Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-50" x=“0” y=“0”></use>
</g>
</svg><b> é distinto de </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.019ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 869.5 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Q</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-51” d=“M53 245Q53 297 70 356T125 478T216 590T349 671T523 703Q656 703 735 637T815 445Q815 410 808 370T781 277T729 178T643 87T519 14L525 4Q540 -19 553 -25T592 -32Q632 -32 654 -24T680 -7T689 10T704 18Q713 18 717 12T722 0Q722 -8 711 -36T681 -101T624 -166T541 -194Q513 -194 494 -183T465 -157T450 -118T444 -79T443 -41V-7L433 -9Q391 -17 344 -17Q301 -17 263 -10T185 15T118 62T71 138T53 245ZM666 482Q666 529 652 563T614 615T565 640T512 648Q412 648 335 573Q268 506 235 389T201 202Q201 164 210 136T230 95T259 66L262 76Q269 109 302 135T382 162Q401 162 415 159T449 140T484 92L491 78L496 82Q502 86 505 88T515 97T528 107T541 120T555 137T570 156T585 179T599 205T612 235Q629 278 647 351T666 482ZM439 56Q439 58 439 62T435 75T426 92T410 106T383 112Q353 112 332 96T311 63Q311 38 355 38H366Q391 39 415 45T439 56Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-51" x=“0” y=“0”></use>
</g>
</svg><b>, e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.968ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 847.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-50” d=“M162 62L302 623Q302 624 258 624H234Q214 624 209 626T200 638Q200 677 217 684Q220 686 439 686Q667 685 684 682Q686 681 693 680Q713 677 733 671T782 649T829 602T847 528Q847 450 784 382T604 293Q571 288 469 287H373L346 176Q340 151 333 122T321 78L317 64Q317 62 361 62H387Q420 62 420 44Q417 10 404 2L399 0L357 1Q331 2 224 2Q149 2 109 1T65 0Q43 0 43 17Q43 21 47 33Q52 54 57 58T89 62H113H162ZM692 558Q692 611 617 622Q610 623 529 624H452L381 343H458H492Q604 343 641 389Q662 414 677 471T692 558Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-50" x=“0” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.019ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 869.5 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Q</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-51” d=“M53 245Q53 297 70 356T125 478T216 590T349 671T523 703Q656 703 735 637T815 445Q815 410 808 370T781 277T729 178T643 87T519 14L525 4Q540 -19 553 -25T592 -32Q632 -32 654 -24T680 -7T689 10T704 18Q713 18 717 12T722 0Q722 -8 711 -36T681 -101T624 -166T541 -194Q513 -194 494 -183T465 -157T450 -118T444 -79T443 -41V-7L433 -9Q391 -17 344 -17Q301 -17 263 -10T185 15T118 62T71 138T53 245ZM666 482Q666 529 652 563T614 615T565 640T512 648Q412 648 335 573Q268 506 235 389T201 202Q201 164 210 136T230 95T259 66L262 76Q269 109 302 135T382 162Q401 162 415 159T449 140T484 92L491 78L496 82Q502 86 505 88T515 97T528 107T541 120T555 137T570 156T585 179T599 205T612 235Q629 278 647 351T666 482ZM439 56Q439 58 439 62T435 75T426 92T410 106T383 112Q353 112 332 96T311 63Q311 38 355 38H366Q391 39 415 45T439 56Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-51" x=“0” y=“0”></use>
</g>
</svg><b> pertencem às retas </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.23ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 529.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-72" x=“0” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.234ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 531.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> s</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-73” d=“M140 290Q140 311 148 336T176 388T235 433T326 451H336Q355 451 373 449T418 439T460 412T476 363Q476 333 456 311T406 289Q384 289 371 302T357 335Q357 351 364 364T379 384L386 391Q386 392 381 394T362 398T330 400Q299 400 278 393T247 373T235 352T232 335Q232 322 242 312Q258 299 315 290T403 260Q457 224 457 167Q457 152 453 134T435 90T397 43T330 7T229 -8Q133 -8 95 22T57 91Q57 127 81 152T139 177Q161 177 177 164T194 121Q189 80 153 56Q179 43 236 43Q275 43 303 52T343 75T361 101T366 124Q366 148 338 161T272 180T232 186Q187 198 164 227T140 290Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-73" x=“0” y=“0”></use>
</g>
</svg><b>, então </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“5.563ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 2395.1 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> r = s</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-73” d=“M140 290Q140 311 148 336T176 388T235 433T326 451H336Q355 451 373 449T418 439T460 412T476 363Q476 333 456 311T406 289Q384 289 371 302T357 335Q357 351 364 364T379 384L386 391Q386 392 381 394T362 398T330 400Q299 400 278 393T247 373T235 352T232 335Q232 322 242 312Q258 299 315 290T403 260Q457 224 457 167Q457 152 453 134T435 90T397 43T330 7T229 -8Q133 -8 95 22T57 91Q57 127 81 152T139 177Q161 177 177 164T194 121Q189 80 153 56Q179 43 236 43Q275 43 303 52T343 75T361 101T366 124Q366 148 338 161T272 180T232 186Q187 198 164 227T140 290Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-72" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“807” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-73" x=“1863” y=“0”></use>
</g>
</svg><b>.</b></p>
<p>Vamos interpretar: temos dois pontos distintos <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.745ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 751.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.838ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 791.5 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Q</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-51” d=“M399 -80Q399 -47 400 -30T402 -11V-7L387 -11Q341 -22 303 -22Q208 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435Q740 255 592 107Q529 47 461 16L444 8V3Q444 2 449 -24T470 -66T516 -82Q551 -82 583 -60T625 -3Q631 11 638 11Q647 11 649 2Q649 -6 639 -34T611 -100T557 -165T481 -194Q399 -194 399 -87V-80ZM636 468Q636 523 621 564T580 625T530 655T477 665Q429 665 379 640Q277 591 215 464T153 216Q153 110 207 59Q231 38 236 38V46Q236 86 269 120T347 155Q372 155 390 144T417 114T429 82T435 55L448 64Q512 108 557 185T619 334T636 468ZM314 18Q362 18 404 39L403 49Q399 104 366 115Q354 117 347 117Q344 117 341 117T337 118Q317 118 296 98T274 52Q274 18 314 18Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-51" x=“0” y=“0”></use>
</g>
</svg>. Eles pertencem a duas retas, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.049ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 451.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-72” d=“M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-72" x=“0” y=“0”></use>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.09ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 469.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> s</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-73” d=“M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-73" x=“0” y=“0”></use>
</g>
</svg>. Isso significa que tanto <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.049ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 451.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-72” d=“M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-72" x=“0” y=“0”></use>
</g>
</svg> quanto <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.09ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 469.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> s</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-73” d=“M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-73" x=“0” y=“0”></use>
</g>
</svg> passam por <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.745ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 751.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.838ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 791.5 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Q</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-51” d=“M399 -80Q399 -47 400 -30T402 -11V-7L387 -11Q341 -22 303 -22Q208 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435Q740 255 592 107Q529 47 461 16L444 8V3Q444 2 449 -24T470 -66T516 -82Q551 -82 583 -60T625 -3Q631 11 638 11Q647 11 649 2Q649 -6 639 -34T611 -100T557 -165T481 -194Q399 -194 399 -87V-80ZM636 468Q636 523 621 564T580 625T530 655T477 665Q429 665 379 640Q277 591 215 464T153 216Q153 110 207 59Q231 38 236 38V46Q236 86 269 120T347 155Q372 155 390 144T417 114T429 82T435 55L448 64Q512 108 557 185T619 334T636 468ZM314 18Q362 18 404 39L403 49Q399 104 366 115Q354 117 347 117Q344 117 341 117T337 118Q317 118 296 98T274 52Q274 18 314 18Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-51" x=“0” y=“0”></use>
</g>
</svg>.</p>
<p>Mas o postulado diz que por dois pontos distintos passa uma única reta. Portanto, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.049ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 451.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-72” d=“M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-72" x=“0” y=“0”></use>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.09ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 469.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> s</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-73” d=“M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-73" x=“0” y=“0”></use>
</g>
</svg> devem ser a mesma reta. A afirmação é <b>verdadeira</b>.</p>
<p>Show?</p>
Passo 4
<p><b>c) Qualquer que seja uma reta </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.23ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 529.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-72" x=“0” y=“0”></use>
</g>
</svg><b>, existem dois pontos </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.019ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 869.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.013ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 866.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-42" x=“0” y=“0”></use>
</g>
</svg><b> tais que </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.019ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 869.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
</g>
</svg><b> é distinto de </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.013ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 866.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-42" x=“0” y=“0”></use>
</g>
</svg><b>, com </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.09ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 2622.1 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A ∈ r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2208” d=“M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2208" x=“1147” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-72" x=“2092” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.083ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 2619.1 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B ∈ r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2208” d=“M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-42" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2208" x=“1144” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-72" x=“2089” y=“0”></use>
</g>
</svg><b>.</b></p>
<p>Uma reta é um conjunto infinito de pontos. Logo, certamente podemos escolher dois pontos distintos sobre ela.</p>
<p>Isso �� um axioma: toda reta tem pelo menos dois pontos. Portanto, é <b>verdadeiro</b>.</p>
<p>Tranquilo?</p>
<title> r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-72" x=“0” y=“0”></use>
</g>
</svg><b>, existem dois pontos </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.019ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 869.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.013ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 866.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-42" x=“0” y=“0”></use>
</g>
</svg><b> tais que </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.019ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 869.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
</g>
</svg><b> é distinto de </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.013ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 866.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-42" x=“0” y=“0”></use>
</g>
</svg><b>, com </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.09ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 2622.1 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A ∈ r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2208” d=“M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2208" x=“1147” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-72" x=“2092” y=“0”></use>
</g>
</svg><b> e </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.083ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 2619.1 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B ∈ r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2208” d=“M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-42" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2208" x=“1144” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-72" x=“2089” y=“0”></use>
</g>
</svg><b>.</b></p>
<p>Uma reta é um conjunto infinito de pontos. Logo, certamente podemos escolher dois pontos distintos sobre ela.</p>
<p>Isso �� um axioma: toda reta tem pelo menos dois pontos. Portanto, é <b>verdadeiro</b>.</p>
<p>Tranquilo?</p>
Passo 5
<p><b>d) Se </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.13ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 3070.1 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A = B</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1147” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-42" x=“2203” y=“0”></use>
</g>
</svg><b>, existe uma reta </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.23ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 529.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-72" x=“0” y=“0”></use>
</g>
</svg><b> tal que </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“9.136ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3933.7 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A , B ∈ r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2C” d=“M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2208” d=“M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2C" x=“869” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-42" x=“1314” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2208" x=“2458” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-72" x=“3404” y=“0”></use>
</g>
</svg><b>.</b></p>
<p>Aqui <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.743ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 750.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-41” d=“M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-41" x=“0” y=“0”></use>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.764ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 759.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-42” d=“M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-42" x=“0” y=“0”></use>
</g>
</svg> são o mesmo ponto. A pergunta é: existe uma reta que contenha esse ponto? Sim, por um ponto passam infinitas retas.</p>
<p>Portanto, existe pelo menos uma reta que contém <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.743ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 750.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-41” d=“M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-41" x=“0” y=“0”></use>
</g>
</svg> (e, consequentemente, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.764ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 759.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-42” d=“M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-42" x=“0” y=“0”></use>
</g>
</svg>, já que são o mesmo). A afirmação é <b>verdadeira</b>.</p>
<p>Entendeu tudo? Responde Aí!</p>
<title> A = B</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1147” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-42" x=“2203” y=“0”></use>
</g>
</svg><b>, existe uma reta </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.23ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 529.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-72" x=“0” y=“0”></use>
</g>
</svg><b> tal que </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“9.136ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3933.7 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A , B ∈ r</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-41” d=“M65 0Q45 0 45 18Q48 52 61 60Q65 62 81 62Q155 62 165 74Q166 74 265 228T465 539T569 699Q576 707 583 709T611 711T637 710T649 700Q650 697 695 380L741 63L784 62H827Q839 50 839 45L835 29Q831 9 827 5T806 0Q803 0 790 0T743 1T657 2Q585 2 547 1T504 0Q481 0 481 17Q484 54 497 60Q501 62 541 62Q580 62 580 63Q580 68 573 121T564 179V181H308L271 124Q236 69 236 67T283 62H287Q316 62 316 46Q316 26 307 8Q302 3 295 0L262 1Q242 2 168 2Q119 2 93 1T65 0ZM537 372Q533 402 528 435T521 486T518 504V505Q517 505 433 375L348 244L451 243Q555 243 555 244L537 372Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2C” d=“M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-42” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 449 686H477H586Q684 686 733 677T817 634Q853 598 853 547Q853 499 826 460T761 401T695 371T654 360H653L662 358Q670 357 683 354T712 344T744 327T774 303T795 269T804 224Q804 148 732 79T533 1Q524 0 288 0H58Q47 5 43 15Q47 54 60 60Q64 62 113 62H162L302 623Q302 624 258 624ZM703 550Q703 571 695 586T675 609T656 619T643 623L545 624H447L417 504Q386 384 386 383T470 382Q554 383 565 385Q632 397 667 447T703 550ZM651 240Q651 265 645 282T626 309T608 322T592 329Q587 330 479 331H373L340 198Q307 65 306 64Q306 62 406 62L507 63L519 65Q565 76 596 107T639 171T651 240Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2208” d=“M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHBI-72” d=“M24 296Q24 298 28 313T42 352T67 398T104 436T154 452Q198 452 230 437T273 404L282 411Q334 452 393 452Q441 452 470 423T500 350Q500 301 473 279T418 256Q395 256 379 270T363 308Q363 366 424 386Q424 388 420 391T405 398T385 401Q363 401 343 390Q321 380 289 341L252 192Q214 42 212 39Q190 -8 142 -8Q117 -8 103 7T89 39Q89 52 127 202T165 369Q165 402 148 402Q139 402 128 393T110 369Q100 348 90 310Q85 289 82 286T60 282H55H44Q24 282 24 296Z”></path>
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<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-41" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2C" x=“869” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-42" x=“1314” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2208" x=“2458” y=“0”></use>
<use xlink:href="#E1-MJMATHBI-72" x=“3404” y=“0”></use>
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</svg><b>.</b></p>
<p>Aqui <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.743ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 750.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-41” d=“M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-41" x=“0” y=“0”></use>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.764ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 759.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-42” d=“M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-42" x=“0” y=“0”></use>
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</svg> são o mesmo ponto. A pergunta é: existe uma reta que contenha esse ponto? Sim, por um ponto passam infinitas retas.</p>
<p>Portanto, existe pelo menos uma reta que contém <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.743ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 750.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> A</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-41” d=“M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-41" x=“0” y=“0”></use>
</g>
</svg> (e, consequentemente, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.764ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 759.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> B</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-42” d=“M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-42" x=“0” y=“0”></use>
</g>
</svg>, já que são o mesmo). A afirmação é <b>verdadeira</b>.</p>
<p>Entendeu tudo? Responde Aí!</p>
Resposta
<p>Todas as afirmações são verdadeiras</p>