111:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000 Pensamiento espacial, métrico y variacional:@0.538113:0.043660:0.926913:0.043660:0.926913:0.024915:0.538113:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Al trabajar con grupos, donde existe uno o varios compañeros con alguna necesidad especial,es importante :@0.097399:0.168129:0.908126:0.168129:0.908126:0.152417:0.097399:0.152417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 hacerles saber que están aprendiendo y que lo han estado haciendo bien.:@0.097399:0.184771:0.633422:0.184771:0.633422:0.169058:0.097399:0.169058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Trabajen:@0.097399:0.216622:0.170160:0.216622:0.170160:0.198905:0.097399:0.198905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en equipo, :@0.170160:0.216622:0.260318:0.216622:0.260318:0.200196:0.170160:0.200196:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 indaguen resuelvan:@0.260318:0.216622:0.437919:0.216622:0.437919:0.198905:0.260318:0.198905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.340123:0.216622:0.357019:0.216622:0.357019:0.200196:0.340123:0.200196:0.000000:0.000000:0.000000 .:@0.437919:0.216622:0.441902:0.216622:0.441902:0.199195:0.437919:0.199195:0.000000 7. :@0.097399:0.247401:0.114407:0.247401:0.114407:0.230731:0.097399:0.230731:0.000000:0.000000:0.000000 Verifiquen:@0.127520:0.247401:0.209762:0.247401:0.209762:0.230454:0.127520:0.230454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la solución y la gráfica. :@0.209672:0.247401:0.386685:0.247401:0.386685:0.230731:0.209672:0.230731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Consideren:@0.127516:0.279252:0.221365:0.279252:0.221365:0.261535:0.127516:0.261535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la circunferencia ( , 2 ) :@0.221269:0.279252:0.415604:0.279252:0.415604:0.262826:0.221269:0.262826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C:@0.352860:0.279252:0.363213:0.279252:0.363213:0.263116:0.352860:0.263116:0.000000 y (1, 1) ( , 2 ).:@0.127516:0.310945:0.274245:0.310945:0.274245:0.294518:0.127516:0.294518:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.152175:0.310365:0.168205:0.310365:0.168205:0.296026:0.152175:0.296026:0.000000 C:@0.212409:0.310945:0.222762:0.310945:0.222762:0.294808:0.212409:0.294808:0.000000 Se tiene || || 2. La ecuación cartesiana de la recta tan-:@0.097399:0.342639:0.524114:0.342639:0.524114:0.326212:0.097399:0.326212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.170141:0.342639:0.179879:0.342639:0.179879:0.326502:0.170141:0.326502:0.000000 :@0.172951:0.343204:0.179359:0.343204:0.179359:0.327343:0.172951:0.327343:0.000000 5:@0.192118:0.342059:0.208148:0.342059:0.208148:0.327720:0.192118:0.327720:0.000000 gente a (0, 2 ) en (1, 1) está definida como: :@0.097399:0.360037:0.494921:0.360037:0.494921:0.343610:0.097399:0.343610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L C:@0.146894:0.360037:0.182380:0.360037:0.182380:0.343900:0.146894:0.343900:0.000000:0.000000:0.000000 :@0.189654:0.358080:0.196063:0.358080:0.196063:0.342219:0.189654:0.342219:0.000000 u:@0.261415:0.360037:0.271153:0.360037:0.271153:0.343900:0.261415:0.343900:0.000000 :@0.264417:0.360603:0.270825:0.360603:0.270825:0.344741:0.264417:0.344741:0.000000 5:@0.275040:0.359457:0.291070:0.359457:0.291070:0.345118:0.275040:0.345118:0.000000 ( , ) , tal que 2.:@0.097399:0.377436:0.314598:0.377436:0.314598:0.361009:0.097399:0.361009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.102499:0.377436:0.125668:0.377436:0.125668:0.361299:0.102499:0.361299:0.000000:0.000000:0.000000 [:@0.134981:0.376988:0.149618:0.376988:0.149618:0.363578:0.134981:0.363578:0.000000 R:@0.153832:0.376418:0.167122:0.376418:0.167122:0.363521:0.153832:0.363521:0.000000 2:@0.167122:0.371095:0.172597:0.371095:0.172597:0.361519:0.167122:0.361519:0.000000 x:@0.237334:0.377436:0.245128:0.377436:0.245128:0.361299:0.237334:0.361299:0.000000 1 5:@0.249342:0.376856:0.297644:0.376856:0.297644:0.362517:0.249342:0.362517:0.000000:0.000000:0.000000 y:@0.269587:0.377436:0.277400:0.377436:0.277400:0.361299:0.269587:0.361299:0.000000 En la Figura 2.18. se muestra el vector (1, 1) y la recta :@0.097392:0.416277:0.552247:0.416277:0.552247:0.399850:0.097392:0.399850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.403722:0.415697:0.419752:0.415697:0.419752:0.401358:0.403722:0.401358:0.000000 L:@0.540065:0.416277:0.548032:0.416277:0.548032:0.400140:0.540065:0.400140:0.000000 tangente a la circunferencia ( , 2 ) en el punto (1, 1).:@0.097397:0.433675:0.542735:0.433675:0.542735:0.417248:0.097397:0.417248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C:@0.313813:0.433675:0.324166:0.433675:0.324166:0.417538:0.313813:0.417538:0.000000 5:@0.482597:0.433095:0.498627:0.433095:0.498627:0.418756:0.482597:0.418756:0.000000 8. Sea ( , 2) la circunferencia de centro 0 y radio 2.:@0.097399:0.464453:0.494006:0.464456:0.494006:0.447786:0.097399:0.447784:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C:@0.158390:0.464453:0.168606:0.464453:0.168606:0.447770:0.158390:0.447770:0.000000 :@0.413275:0.462473:0.417877:0.462473:0.417877:0.447301:0.413275:0.447301:0.000000 a. :@0.128943:0.495391:0.144387:0.495391:0.144387:0.479678:0.128943:0.479678:0.000000:0.000000:0.000000 Consideren:@0.159145:0.495391:0.248913:0.495391:0.248913:0.478444:0.159145:0.478444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (0, 2) y ( 2, 0). :@0.248825:0.495391:0.431020:0.495391:0.431020:0.479678:0.248825:0.479678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.260587:0.498563:0.265824:0.498563:0.265824:0.489403:0.260587:0.489403:0.000000 5:@0.269533:0.494836:0.284866:0.494836:0.284866:0.481120:0.269533:0.481120:0.000000 2:@0.346365:0.498563:0.351602:0.498563:0.351602:0.489403:0.346365:0.489403:0.000000 5 2:@0.355311:0.494836:0.394445:0.494836:0.394445:0.481120:0.355311:0.481120:0.000000:0.000000:0.000000 Determinen:@0.430726:0.495391:0.525411:0.495391:0.525411:0.478444:0.430726:0.478444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las :@0.525320:0.495391:0.552085:0.495391:0.552085:0.479678:0.525320:0.479678:0.000000:0.000000:0.000000:0.000000:0.000000 ecuaciones cartesianas de las rectas tangentes , a :@0.159071:0.512033:0.552060:0.512033:0.552060:0.496320:0.159071:0.496320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L L:@0.502256:0.512033:0.530152:0.512033:0.530152:0.496597:0.502256:0.496597:0.000000:0.000000:0.000000 1:@0.509820:0.515205:0.515057:0.515205:0.515057:0.506045:0.509820:0.506045:0.000000 2:@0.530100:0.515205:0.535336:0.515205:0.535336:0.506045:0.530100:0.506045:0.000000 la circunferencia ( , 2) en los puntos y .:@0.159056:0.528675:0.479568:0.528675:0.479568:0.512962:0.159056:0.512962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C:@0.280967:0.528675:0.290871:0.528675:0.290871:0.513239:0.280967:0.513239:0.000000 1:@0.442054:0.531847:0.447291:0.531847:0.447291:0.522686:0.442054:0.522686:0.000000 2:@0.471176:0.531847:0.476413:0.531847:0.476413:0.522686:0.471176:0.522686:0.000000 b. :@0.128943:0.560368:0.145842:0.560368:0.145842:0.544656:0.128943:0.544656:0.000000:0.000000:0.000000 Verifiquen:@0.159145:0.560368:0.241387:0.560368:0.241387:0.543421:0.159145:0.543421:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que si ( , ) , :@0.241297:0.560368:0.400349:0.560368:0.400349:0.544656:0.241297:0.544656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.303096:0.559814:0.318430:0.559814:0.318430:0.546098:0.303096:0.546098:0.000000 x y:@0.326731:0.560368:0.348305:0.560368:0.348305:0.544933:0.326731:0.544933:0.000000:0.000000:0.000000 [:@0.356651:0.560078:0.371288:0.560078:0.371288:0.546668:0.356651:0.546668:0.000000 R:@0.374808:0.559509:0.388098:0.559509:0.388098:0.546611:0.374808:0.546611:0.000000 2:@0.387999:0.554305:0.393236:0.554305:0.393236:0.545144:0.387999:0.545144:0.000000 entonces, 2 :@0.399912:0.560526:0.552239:0.560526:0.552239:0.544099:0.399912:0.544099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ? 5:@0.488954:0.559946:0.527241:0.559946:0.527241:0.545607:0.488954:0.545607:0.000000:0.000000:0.000000 y:@0.540211:0.560526:0.548024:0.560526:0.548024:0.544389:0.540211:0.544389:0.000000 y 2 . La ecuación cartesiana de está :@0.159065:0.577924:0.552261:0.577924:0.552261:0.561497:0.159065:0.561497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.181706:0.581240:0.187181:0.581240:0.187181:0.571663:0.181706:0.571663:0.000000 ?:@0.193044:0.577344:0.199452:0.577344:0.199452:0.563005:0.193044:0.563005:0.000000 5 2:@0.219809:0.577344:0.257835:0.577344:0.257835:0.563005:0.219809:0.563005:0.000000:0.000000:0.000000 x:@0.267630:0.577924:0.275424:0.577924:0.275424:0.561787:0.267630:0.561787:0.000000 L:@0.496825:0.577924:0.504792:0.577924:0.504792:0.561787:0.496825:0.561787:0.000000 1:@0.504937:0.581240:0.510412:0.581240:0.510412:0.571663:0.504937:0.571663:0.000000 definida como: ( , ) :@0.159069:0.595323:0.349673:0.595323:0.349673:0.578896:0.159069:0.578896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.292198:0.595323:0.318274:0.595323:0.318274:0.579186:0.292198:0.579186:0.000000:0.000000:0.000000 [:@0.330491:0.594875:0.345128:0.594875:0.345128:0.581465:0.330491:0.581465:0.000000 R:@0.351999:0.594305:0.365289:0.594305:0.365289:0.581408:0.351999:0.581408:0.000000 2:@0.365636:0.588982:0.371111:0.588982:0.371111:0.579406:0.365636:0.579406:0.000000 , 2 4 o 2, y la :@0.371297:0.595323:0.552267:0.595323:0.552267:0.578896:0.371297:0.578896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.391214:0.595323:0.399027:0.595323:0.399027:0.579186:0.391214:0.579186:0.000000 5:@0.405840:0.594743:0.421870:0.594743:0.421870:0.580404:0.405840:0.580404:0.000000 y:@0.462128:0.595323:0.469941:0.595323:0.469941:0.579186:0.462128:0.579186:0.000000 5:@0.476734:0.594743:0.492765:0.594743:0.492765:0.580404:0.476734:0.580404:0.000000 ecuación cartesiana de :@0.159075:0.612721:0.370833:0.612721:0.370833:0.596294:0.159075:0.596294:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.377012:0.612721:0.384979:0.612721:0.384979:0.596584:0.377012:0.596584:0.000000 2:@0.385763:0.616037:0.391238:0.616037:0.391238:0.606460:0.385763:0.606460:0.000000 está dada como :@0.391799:0.612721:0.552255:0.612721:0.552255:0.596294:0.391799:0.596294:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.548022:0.612721:0.552236:0.612721:0.552236:0.596294:0.548022:0.596294:0.000000 ( , ) , 2 4 o 2.:@0.159063:0.630119:0.386187:0.630119:0.386187:0.613692:0.159063:0.613692:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.164086:0.630119:0.187005:0.630119:0.187005:0.613982:0.164086:0.613982:0.000000:0.000000:0.000000 [:@0.196088:0.629672:0.210725:0.629672:0.210725:0.616262:0.196088:0.616262:0.000000 R:@0.214767:0.629102:0.228057:0.629102:0.228057:0.616204:0.214767:0.616204:0.000000 2:@0.227965:0.623779:0.233440:0.623779:0.233440:0.614202:0.227965:0.614202:0.000000 2:@0.240779:0.629539:0.256810:0.629539:0.256810:0.615200:0.240779:0.615200:0.000000 x:@0.266027:0.630119:0.273821:0.630119:0.273821:0.613982:0.266027:0.613982:0.000000 5:@0.277882:0.629539:0.293912:0.629539:0.293912:0.615200:0.277882:0.615200:0.000000 x:@0.325664:0.630119:0.333458:0.630119:0.333458:0.613982:0.325664:0.613982:0.000000 5 2:@0.337519:0.629539:0.373620:0.629539:0.373620:0.615200:0.337519:0.615200:0.000000:0.000000:0.000000 c. :@0.128943:0.660898:0.144019:0.660898:0.144019:0.645185:0.128943:0.645185:0.000000:0.000000:0.000000 Comprueben:@0.159145:0.660898:0.267737:0.660898:0.267737:0.643951:0.159145:0.643951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 si en la Figura 2.19. se muestra la :@0.268245:0.660898:0.552173:0.660898:0.552173:0.645185:0.268245:0.645185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 circunferencia ( , 2), los puntos , , y las rectas :@0.159071:0.677539:0.552044:0.677539:0.552044:0.661827:0.159071:0.661827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C:@0.273215:0.677539:0.283118:0.677539:0.283118:0.662104:0.273215:0.662104:0.000000 2:@0.446060:0.680712:0.451297:0.680712:0.451297:0.671551:0.446060:0.671551:0.000000 tangentes y .:@0.159055:0.694181:0.284947:0.694181:0.284947:0.678469:0.159055:0.678469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.236365:0.694181:0.243986:0.694181:0.243986:0.678746:0.236365:0.678746:0.000000 1:@0.243932:0.697354:0.249169:0.697354:0.249169:0.688193:0.243932:0.688193:0.000000 L:@0.265045:0.694181:0.272666:0.694181:0.272666:0.678746:0.265045:0.678746:0.000000 2:@0.272597:0.697354:0.277834:0.697354:0.277834:0.688193:0.272597:0.688193:0.000000 Trabajo colaborativo:@0.089309:0.139215:0.244769:0.139215:0.244769:0.122546:0.089309:0.122546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 9. :@0.082043:0.785392:0.099051:0.785392:0.099051:0.768723:0.082043:0.768723:0.000000:0.000000:0.000000 Analiza decide:@0.112164:0.785392:0.239432:0.785392:0.239432:0.768446:0.112164:0.768446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.170202:0.785392:0.186529:0.785392:0.186529:0.768723:0.170202:0.768723:0.000000:0.000000:0.000000 si las afirmaciones son verdaderas (V) o falsas (F). :@0.239339:0.785392:0.615188:0.785392:0.615188:0.768723:0.239339:0.768723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 V:@0.838798:0.811062:0.849069:0.811062:0.849069:0.794393:0.838798:0.794393:0.000000 F:@0.882294:0.811062:0.891258:0.811062:0.891258:0.794393:0.882294:0.794393:0.000000 Para encontrar la ecuación cartesiana de una circunferencia con centro distinto al origen (0, 0), se :@0.089162:0.836081:0.819717:0.836081:0.819717:0.820368:0.089162:0.820368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 aplica la siguiente fórmula: .:@0.089162:0.852723:0.370956:0.852721:0.370956:0.837009:0.089162:0.837010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.285899:0.852723:0.293354:0.852723:0.293354:0.837287:0.285899:0.837287:0.000000 2:@0.293275:0.846657:0.298512:0.846657:0.298512:0.837497:0.293275:0.837497:0.000000 1:@0.302424:0.852167:0.317757:0.852167:0.317757:0.838451:0.302424:0.838451:0.000000 y:@0.321622:0.852721:0.329096:0.852721:0.329096:0.837286:0.321622:0.837286:0.000000 2:@0.329015:0.846657:0.334252:0.846657:0.334252:0.837497:0.329015:0.837497:0.000000 5:@0.338162:0.852167:0.353495:0.852167:0.353495:0.838451:0.338162:0.838451:0.000000 r:@0.357361:0.852721:0.362644:0.852721:0.362644:0.837286:0.357361:0.837286:0.000000 2:@0.362563:0.846657:0.367800:0.846657:0.367800:0.837497:0.362563:0.837497:0.000000 Se puede calcular la ecuación de una circunferencia si se conocen tres puntos que le pertenecen.:@0.089159:0.875479:0.793214:0.875479:0.793214:0.859766:0.089159:0.859766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si se tiene tan solo el punto medio del diámetro de una circunferencia se puede calcular la ecuación :@0.089159:0.898237:0.820374:0.898237:0.820374:0.882524:0.089159:0.882524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de la circunferencia.:@0.089159:0.914879:0.233174:0.914879:0.233174:0.899166:0.089159:0.899166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Actividad indagatoria:@0.085363:0.762379:0.248724:0.762379:0.248724:0.745709:0.085363:0.745709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Figura 3.8:@0.853021:0.488197:0.904348:0.488197:0.904348:0.476770:0.853021:0.476770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.687452:0.380223:0.693984:0.380223:0.693984:0.368796:0.687452:0.368796:0.000000 2:@0.676300:0.437001:0.687452:0.437001:0.687452:0.427026:0.676300:0.427026:0.000000 1:@0.687452:0.437404:0.693984:0.437404:0.693984:0.425977:0.687452:0.425977:0.000000 2:@0.676300:0.465594:0.687452:0.465594:0.687452:0.455619:0.676300:0.455619:0.000000 2:@0.687452:0.465998:0.693984:0.465998:0.693984:0.454570:0.687452:0.454570:0.000000 2:@0.687452:0.351633:0.693984:0.351633:0.693984:0.340206:0.687452:0.340206:0.000000 3:@0.687452:0.323039:0.693984:0.323039:0.693984:0.311612:0.687452:0.311612:0.000000 1:@0.735618:0.418745:0.742151:0.418745:0.742151:0.407318:0.735618:0.407318:0.000000 2:@0.654144:0.418342:0.665296:0.418342:0.665296:0.408367:0.654144:0.408367:0.000000 1:@0.665296:0.418745:0.671829:0.418745:0.671829:0.407318:0.665296:0.407318:0.000000 2:@0.616192:0.418342:0.627343:0.418342:0.627343:0.408367:0.616192:0.408367:0.000000 2:@0.627343:0.418745:0.633876:0.418745:0.633876:0.407318:0.627343:0.407318:0.000000 x:@0.605568:0.451745:0.612345:0.451745:0.612345:0.437713:0.605568:0.437713:0.000000 2:@0.612345:0.446233:0.617106:0.446233:0.617106:0.437905:0.612345:0.437905:0.000000 2:@0.617106:0.451745:0.679364:0.451745:0.679364:0.437461:0.617106:0.437461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.620770:0.451241:0.634710:0.451241:0.634710:0.438772:0.620770:0.438772:0.000000 y:@0.638374:0.451745:0.645168:0.451745:0.645168:0.437713:0.638374:0.437713:0.000000 2:@0.645168:0.446233:0.649929:0.446233:0.649929:0.437905:0.645168:0.437905:0.000000 5:@0.653594:0.451241:0.667533:0.451241:0.667533:0.438772:0.653594:0.438772:0.000000 x:@0.829802:0.440235:0.836579:0.440235:0.836579:0.426202:0.829802:0.426202:0.000000 2:@0.836579:0.440235:0.894076:0.440235:0.894076:0.425950:0.836579:0.425950:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 5:@0.840243:0.439730:0.882245:0.439730:0.882245:0.427261:0.840243:0.427261:0.000000:0.000000:0.000000 y:@0.857847:0.440235:0.864641:0.440235:0.864641:0.426202:0.857847:0.426202:0.000000 L:@0.723642:0.360278:0.730570:0.360278:0.730570:0.346246:0.723642:0.346246:0.000000 2:@0.773566:0.418745:0.780099:0.418745:0.780099:0.407318:0.773566:0.407318:0.000000 3:@0.811518:0.418745:0.818051:0.418745:0.818051:0.407318:0.811518:0.407318:0.000000 4:@0.849470:0.418745:0.856003:0.418745:0.856003:0.407318:0.849470:0.407318:0.000000 0:@0.689133:0.404268:0.696891:0.404268:0.696891:0.390698:0.689133:0.390698:0.000000 y:@0.688895:0.312823:0.695890:0.312823:0.695890:0.299253:0.688895:0.299253:0.000000 x:@0.885384:0.419395:0.892204:0.419395:0.892204:0.405825:0.885384:0.405825:0.000000 u:@0.721888:0.403057:0.730652:0.403057:0.730652:0.388534:0.721888:0.388534:0.000000 :@0.724590:0.403566:0.730357:0.403566:0.730357:0.389291:0.724590:0.389291:0.000000 Figura 3.9:@0.853450:0.680733:0.904776:0.680733:0.904776:0.669306:0.853450:0.669306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.688414:0.583062:0.694947:0.583062:0.694947:0.571634:0.688414:0.571634:0.000000 2:@0.677264:0.639838:0.688415:0.639838:0.688415:0.629863:0.677264:0.629863:0.000000 1:@0.688415:0.640242:0.694948:0.640242:0.694948:0.628814:0.688415:0.628814:0.000000 2:@0.677264:0.668432:0.688415:0.668432:0.688415:0.658457:0.677264:0.658457:0.000000 2:@0.688415:0.668835:0.694948:0.668835:0.694948:0.657408:0.688415:0.657408:0.000000 2:@0.688415:0.554471:0.694948:0.554471:0.694948:0.543043:0.688415:0.543043:0.000000 3:@0.688415:0.525877:0.694948:0.525877:0.694948:0.514450:0.688415:0.514450:0.000000 1:@0.736582:0.621583:0.743115:0.621583:0.743115:0.610155:0.736582:0.610155:0.000000 2:@0.655108:0.621179:0.666260:0.621179:0.666260:0.611204:0.655108:0.611204:0.000000 1:@0.666260:0.621583:0.672793:0.621583:0.672793:0.610155:0.666260:0.610155:0.000000 2:@0.617156:0.621179:0.628307:0.621179:0.628307:0.611204:0.617156:0.611204:0.000000 2:@0.628307:0.621583:0.634840:0.621583:0.634840:0.610155:0.628307:0.610155:0.000000 L:@0.828274:0.545666:0.835202:0.545666:0.835202:0.531633:0.828274:0.531633:0.000000 1:@0.835202:0.548550:0.839962:0.548550:0.839962:0.540222:0.835202:0.540222:0.000000 L:@0.610576:0.523681:0.617504:0.523681:0.617504:0.509649:0.610576:0.509649:0.000000 2:@0.617502:0.526565:0.622263:0.526565:0.622263:0.518237:0.617502:0.518237:0.000000 2:@0.774530:0.621583:0.781062:0.621583:0.781062:0.610155:0.774530:0.610155:0.000000 3:@0.812482:0.621583:0.819015:0.621583:0.819015:0.610155:0.812482:0.610155:0.000000 4:@0.850434:0.621583:0.856967:0.621583:0.856967:0.610155:0.850434:0.610155:0.000000 0:@0.690095:0.607107:0.697853:0.607107:0.697853:0.593537:0.690095:0.593537:0.000000 y:@0.687298:0.512428:0.694292:0.512428:0.694292:0.498858:0.687298:0.498858:0.000000 x:@0.886346:0.622234:0.893166:0.622234:0.893166:0.608664:0.886346:0.608664:0.000000 u:@0.711262:0.593279:0.720026:0.593279:0.720026:0.578756:0.711262:0.578756:0.000000 :@0.713965:0.593788:0.719732:0.593788:0.719732:0.579513:0.713965:0.579513:0.000000 1:@0.719731:0.596234:0.724635:0.596234:0.724635:0.587657:0.719731:0.587657:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000