157:@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, numérico y variacional:@0.444620:0.043661:0.926912:0.043661:0.926912:0.024916:0.444620:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3.1 Aplicación de vectores en la física:@0.073089:0.240833:0.362882:0.240833:0.362882:0.223886:0.073089:0.223886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En esta sección, se tratan algunos problemas de la geometría y se presentan soluciones :@0.073089:0.267487:0.710880:0.267487:0.710880:0.251053:0.073089:0.251053:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 mediante la aplicación de los vectores geométricos en el plano, junto con sus :@0.073089:0.284129:0.710845:0.284129:0.710845:0.267695:0.073089:0.267695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 operaciones y propiedades.:@0.073089:0.300771:0.272866:0.300771:0.272866:0.284337:0.073089:0.284337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejercicio resuelto:@0.073089:0.328133:0.201667:0.328133:0.201667:0.311463:0.073089:0.311463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Demuestra que el segmento que une los puntos medios de dos lados de un triángulo es :@0.073089:0.355495:0.710035:0.355495:0.710035:0.339061:0.073089:0.339061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 paralelo al tercer lado e igual a la mitad.:@0.073089:0.372137:0.359101:0.372137:0.359101:0.355703:0.073089:0.355703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Demostración:@0.073089:0.399499:0.180339:0.399499:0.180339:0.382829:0.073089:0.382829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Considérese el triángulo, de la Figura 3.1. de vértices :@0.073089:0.426861:0.451207:0.426861:0.451207:0.410427:0.073089:0.410427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A, B, C.:@0.450456:0.426861:0.494392:0.426861:0.494392:0.410454:0.450456:0.410454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A los lados del triángulo los :@0.494357:0.426861:0.710385:0.426861:0.710385:0.410427:0.494357:0.410427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 T:@0.674270:0.426861:0.682387:0.426861:0.682387:0.410454:0.674270:0.410454:0.000000 denotamos con , , , y , y, con estos, asociamos los vectores :@0.073089:0.443502:0.584439:0.443502:0.584439:0.427069:0.073089:0.427069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.192644:0.444085:0.196730:0.444085:0.196730:0.426431:0.192644:0.426431:0.000000 A B A C:@0.196638:0.443502:0.264672:0.443502:0.264672:0.427096:0.196638:0.427096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4 3:@0.222464:0.444085:0.237797:0.444085:0.237797:0.426431:0.222464:0.426431:0.000000:0.000000:0.000000 4 3:@0.264598:0.444085:0.288969:0.444085:0.288969:0.426431:0.264598:0.426431:0.000000:0.000000:0.000000 B C:@0.288877:0.443502:0.314794:0.443502:0.314794:0.427096:0.288877:0.427096:0.000000:0.000000:0.000000 4:@0.314721:0.444085:0.318807:0.444085:0.318807:0.426431:0.314721:0.426431:0.000000 AB AC BC:@0.584369:0.443502:0.664514:0.443502:0.664514:0.427096:0.584369:0.427096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , :@0.602960:0.443502:0.610120:0.443502:0.610120:0.427069:0.602960:0.427069:0.000000:0.000000 y :@0.629559:0.443502:0.645748:0.443502:0.645748:0.427069:0.629559:0.427069:0.000000:0.000000:0.000000 . En la :@0.664459:0.443502:0.710385:0.443502:0.710385:0.427069:0.664459:0.427069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Figura 3.1. se muestran el triángulo , los vectores , :@0.073052:0.460144:0.456181:0.460144:0.456181:0.443710:0.073052:0.443710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 T:@0.327017:0.460144:0.335135:0.460144:0.335135:0.443738:0.327017:0.443738:0.000000 AB AC BC:@0.430429:0.460144:0.508825:0.460144:0.508825:0.443738:0.430429:0.443738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y , y los puntos medios de los :@0.475048:0.460144:0.710488:0.460144:0.710488:0.443710:0.475048:0.443710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 segmentos , y , .:@0.073052:0.476786:0.245510:0.476786:0.245510:0.460352:0.073052:0.460352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.158038:0.477368:0.162125:0.477368:0.162125:0.459714:0.158038:0.459714:0.000000 A C:@0.162033:0.476786:0.188815:0.476786:0.188815:0.460380:0.162033:0.460380:0.000000:0.000000:0.000000 4 3:@0.188742:0.477368:0.212745:0.477368:0.212745:0.459714:0.188742:0.459714:0.000000:0.000000:0.000000 B C:@0.212653:0.476786:0.238386:0.476786:0.238386:0.460380:0.212653:0.460380:0.000000:0.000000:0.000000 4:@0.238312:0.477368:0.242399:0.477368:0.242399:0.459714:0.238312:0.459714:0.000000 Sea el punto medio del segmento , , y el punto medio del segmento , . :@0.073015:0.504148:0.710293:0.504148:0.710293:0.487714:0.073015:0.487714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 D:@0.104989:0.504148:0.116512:0.504148:0.116512:0.487742:0.104989:0.487742:0.000000 3:@0.357334:0.504730:0.361420:0.504730:0.361420:0.487076:0.357334:0.487076:0.000000 A C:@0.361623:0.504148:0.390467:0.504148:0.390467:0.487742:0.361623:0.487742:0.000000:0.000000:0.000000 4:@0.390614:0.504730:0.394700:0.504730:0.394700:0.487076:0.390614:0.487076:0.000000 E:@0.417599:0.504148:0.425717:0.504148:0.425717:0.487742:0.417599:0.487742:0.000000 3:@0.666539:0.504730:0.670625:0.504730:0.670625:0.487076:0.666539:0.487076:0.000000 B C:@0.670828:0.504148:0.698623:0.504148:0.698623:0.487742:0.670828:0.487742:0.000000:0.000000:0.000000 4:@0.698770:0.504730:0.702856:0.504730:0.702856:0.487076:0.698770:0.487076:0.000000 Entonces, :@0.073015:0.525352:0.149210:0.525352:0.149210:0.508919:0.073015:0.508919:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AD:@0.150528:0.525352:0.172065:0.525352:0.172065:0.508946:0.150528:0.508946:0.000000:0.000000 :@0.172194:0.525352:0.176225:0.525352:0.176225:0.508919:0.172194:0.508919:0.000000 5 :@0.177587:0.524798:0.197706:0.524798:0.197706:0.511082:0.177587:0.511082:0.000000:0.000000 1:@0.203023:0.519109:0.212006:0.519109:0.212006:0.502675:0.203023:0.502675:0.000000 2:@0.203023:0.533088:0.212006:0.533088:0.212006:0.516655:0.203023:0.516655:0.000000 :@0.215834:0.525350:0.219865:0.525350:0.219865:0.508916:0.215834:0.508916:0.000000 AC BE:@0.221228:0.525350:0.266804:0.525350:0.266804:0.508944:0.221228:0.508944:0.000000:0.000000:0.000000:0.000000:0.000000 , :@0.240960:0.525350:0.248360:0.525350:0.248360:0.508916:0.240960:0.508916:0.000000:0.000000 :@0.266933:0.525350:0.313766:0.525350:0.313766:0.508916:0.266933:0.508916:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.272326:0.524795:0.287659:0.524795:0.287659:0.511080:0.272326:0.511080:0.000000 1:@0.296923:0.519109:0.305906:0.519109:0.305906:0.502675:0.296923:0.502675:0.000000 2:@0.296923:0.533088:0.305906:0.533088:0.305906:0.516655:0.296923:0.516655:0.000000 BC:@0.315128:0.525350:0.333995:0.525350:0.333995:0.508944:0.315128:0.508944:0.000000:0.000000 . Mostremos que :@0.334124:0.525350:0.465670:0.525350:0.465670:0.508916:0.334124:0.508916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 DE:@0.466988:0.525350:0.486757:0.525350:0.486757:0.508944:0.466988:0.508944:0.000000:0.000000 :@0.486886:0.525350:0.533714:0.525350:0.533714:0.508916:0.486886:0.508916:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.492279:0.524795:0.507613:0.524795:0.507613:0.511080:0.492279:0.511080:0.000000 1:@0.516872:0.519109:0.525854:0.519109:0.525854:0.502675:0.516872:0.502675:0.000000 2:@0.516872:0.533088:0.525854:0.533088:0.525854:0.516655:0.516872:0.516655:0.000000 AB:@0.535076:0.525350:0.553925:0.525350:0.553925:0.508944:0.535076:0.508944:0.000000:0.000000 y, en consecuencia, :@0.554054:0.525350:0.710435:0.525350:0.710435:0.508916:0.554054:0.508916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.706337:0.525350:0.710369:0.525350:0.710369:0.508916:0.706337:0.508916:0.000000 3:@0.073091:0.542574:0.077177:0.542574:0.077177:0.524920:0.073091:0.524920:0.000000 D E:@0.077085:0.541992:0.103721:0.541992:0.103721:0.525586:0.077085:0.525586:0.000000:0.000000:0.000000 , || A, B .:@0.088535:0.541992:0.161335:0.541992:0.161335:0.525558:0.088535:0.525558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4 3:@0.103647:0.542574:0.127264:0.542574:0.127264:0.524920:0.103647:0.524920:0.000000:0.000000:0.000000 4:@0.154138:0.542574:0.158225:0.542574:0.158225:0.524920:0.154138:0.524920:0.000000 De la suma de vectores :@0.073054:0.569354:0.275324:0.569354:0.275324:0.552920:0.073054:0.552920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AB :@0.279503:0.569354:0.302567:0.569354:0.302567:0.552948:0.279503:0.552948:0.000000:0.000000:0.000000 1:@0.305998:0.568799:0.321331:0.568799:0.321331:0.555083:0.305998:0.555083:0.000000 :@0.322049:0.569354:0.326080:0.569354:0.326080:0.552920:0.322049:0.552920:0.000000 BC :@0.330259:0.569354:0.353341:0.569354:0.353341:0.552948:0.330259:0.552948:0.000000:0.000000:0.000000 5:@0.356765:0.568799:0.372098:0.568799:0.372098:0.555083:0.356765:0.555083:0.000000 AC:@0.372816:0.569354:0.399544:0.569354:0.399544:0.552948:0.372816:0.552948:0.000000:0.000000:0.000000:0.000000 , se obtiene :@0.400059:0.569354:0.502965:0.569354:0.502965:0.552920:0.400059:0.552920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AB :@0.507143:0.569354:0.530208:0.569354:0.530208:0.552948:0.507143:0.552948:0.000000:0.000000:0.000000 5:@0.533641:0.568799:0.548974:0.568799:0.548974:0.555083:0.533641:0.555083:0.000000 :@0.549692:0.569354:0.553723:0.569354:0.553723:0.552920:0.549692:0.552920:0.000000 BC :@0.557901:0.569354:0.580984:0.569354:0.580984:0.552948:0.557901:0.552948:0.000000:0.000000:0.000000 5:@0.584408:0.568799:0.599741:0.568799:0.599741:0.555083:0.584408:0.555083:0.000000 AC:@0.600459:0.569354:0.627186:0.569354:0.627186:0.552948:0.600459:0.552948:0.000000:0.000000:0.000000:0.000000 . Además, :@0.627702:0.569354:0.710350:0.569354:0.710350:0.552920:0.627702:0.552920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AB :@0.073073:0.585996:0.094959:0.585996:0.094959:0.569589:0.073073:0.569589:0.000000:0.000000:0.000000 1:@0.094904:0.585441:0.110237:0.585441:0.110237:0.571725:0.094904:0.571725:0.000000 :@0.110145:0.585996:0.114176:0.585996:0.114176:0.569562:0.110145:0.569562:0.000000 BE AD:@0.114102:0.585996:0.173981:0.585996:0.173981:0.569589:0.114102:0.569589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.134166:0.585441:0.149500:0.585441:0.149500:0.571725:0.134166:0.571725:0.000000 :@0.173926:0.585996:0.197156:0.585996:0.197156:0.569562:0.173926:0.569562:0.000000:0.000000:0.000000 1:@0.177884:0.585441:0.193217:0.585441:0.193217:0.571725:0.177884:0.571725:0.000000 DE :@0.197082:0.585996:0.219889:0.585996:0.219889:0.569589:0.197082:0.569589:0.000000:0.000000:0.000000 (véase la Figura 3.1.). Luego, :@0.219834:0.585996:0.423370:0.585996:0.423370:0.569562:0.219834:0.569562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AC:@0.276970:0.617920:0.296371:0.617920:0.296371:0.601514:0.276970:0.601514:0.000000:0.000000 :@0.296316:0.617920:0.319546:0.617920:0.319546:0.601486:0.296316:0.601486:0.000000:0.000000:0.000000 2:@0.300273:0.617365:0.315607:0.617365:0.315607:0.603650:0.300273:0.603650:0.000000 BC :@0.319472:0.617920:0.359876:0.617920:0.359876:0.601514:0.319472:0.601514:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.341322:0.617365:0.356655:0.617365:0.356655:0.603650:0.341322:0.603650:0.000000 1:@0.363475:0.611681:0.372458:0.611681:0.372458:0.595247:0.363475:0.595247:0.000000 2:@0.363475:0.625660:0.372458:0.625660:0.372458:0.609226:0.363475:0.609226:0.000000 :@0.376048:0.617921:0.380079:0.617921:0.380079:0.601488:0.376048:0.601488:0.000000 BC :@0.380005:0.617921:0.401910:0.617921:0.401910:0.601515:0.380005:0.601515:0.000000:0.000000:0.000000 5 :@0.401855:0.617367:0.421698:0.617367:0.421698:0.603651:0.401855:0.603651:0.000000:0.000000 1:@0.425275:0.611681:0.434258:0.611681:0.434258:0.595247:0.425275:0.595247:0.000000 2:@0.425275:0.625660:0.434258:0.625660:0.434258:0.609226:0.425275:0.609226:0.000000 :@0.437847:0.617921:0.441879:0.617921:0.441879:0.601488:0.437847:0.601488:0.000000 AC DE:@0.441805:0.617921:0.502439:0.617921:0.502439:0.601515:0.441805:0.601515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.464391:0.617367:0.479724:0.617367:0.479724:0.603651:0.464391:0.603651:0.000000 y de esta igualdad se tiene :@0.073089:0.645283:0.269495:0.645283:0.269495:0.628850:0.073089:0.628850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 DE:@0.269219:0.645283:0.288786:0.645283:0.288786:0.628877:0.269219:0.628877:0.000000:0.000000 ::@0.288730:0.645283:0.291933:0.645283:0.291933:0.628850:0.288730:0.628850:0.000000 DE:@0.217973:0.677208:0.237540:0.677208:0.237540:0.660802:0.217973:0.660802:0.000000:0.000000 :@0.237485:0.677208:0.260714:0.677208:0.260714:0.660774:0.237485:0.660774:0.000000:0.000000:0.000000 5:@0.241442:0.676653:0.256775:0.676653:0.256775:0.662938:0.241442:0.662938:0.000000 AC:@0.260641:0.677208:0.280042:0.677208:0.280042:0.660802:0.260641:0.660802:0.000000:0.000000 :@0.279987:0.677208:0.284018:0.677208:0.284018:0.660774:0.279987:0.660774:0.000000 2:@0.283944:0.676653:0.299278:0.676653:0.299278:0.662938:0.283944:0.662938:0.000000 1:@0.302834:0.670968:0.311816:0.670968:0.311816:0.654535:0.302834:0.654535:0.000000 2:@0.302834:0.684948:0.311816:0.684948:0.311816:0.668514:0.302834:0.668514:0.000000 :@0.315406:0.677209:0.319437:0.677209:0.319437:0.660775:0.315406:0.660775:0.000000 AC BC :@0.319363:0.677209:0.400834:0.677209:0.400834:0.660803:0.319363:0.660803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.341949:0.676654:0.357282:0.676654:0.357282:0.662939:0.341949:0.662939:0.000000 1:@0.382279:0.676654:0.397613:0.676654:0.397613:0.662939:0.382279:0.662939:0.000000 1:@0.404447:0.670968:0.413429:0.670968:0.413429:0.654535:0.404447:0.654535:0.000000 2:@0.404447:0.684948:0.413429:0.684948:0.413429:0.668514:0.404447:0.668514:0.000000 :@0.417019:0.677209:0.421050:0.677209:0.421050:0.660775:0.417019:0.660775:0.000000 BC :@0.420976:0.677209:0.461380:0.677209:0.461380:0.660803:0.420976:0.660803:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.442826:0.676654:0.458159:0.676654:0.458159:0.662939:0.442826:0.662939:0.000000 1:@0.464983:0.670968:0.473966:0.670968:0.473966:0.654535:0.464983:0.654535:0.000000 2:@0.464983:0.684948:0.473966:0.684948:0.473966:0.668514:0.464983:0.668514:0.000000 :@0.477555:0.677209:0.481586:0.677209:0.481586:0.660775:0.477555:0.660775:0.000000 AC :@0.481513:0.677209:0.522653:0.677209:0.522653:0.660803:0.481513:0.660803:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.504099:0.676654:0.519432:0.676654:0.519432:0.662939:0.504099:0.662939:0.000000 1:@0.526256:0.670968:0.535239:0.670968:0.535239:0.654535:0.526256:0.654535:0.000000 2:@0.526256:0.684948:0.535239:0.684948:0.535239:0.668514:0.526256:0.668514:0.000000 :@0.538828:0.677209:0.542859:0.677209:0.542859:0.660775:0.538828:0.660775:0.000000 BC:@0.542786:0.677209:0.561451:0.677209:0.561451:0.660803:0.542786:0.660803:0.000000:0.000000 DE:@0.292668:0.709134:0.312235:0.709134:0.312235:0.692728:0.292668:0.692728:0.000000:0.000000 (:@0.312179:0.709134:0.360386:0.709134:0.360386:0.692700:0.312179:0.692700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.316137:0.708579:0.331470:0.708579:0.331470:0.694863:0.316137:0.694863:0.000000 1:@0.338979:0.702893:0.347962:0.702893:0.347962:0.686459:0.338979:0.686459:0.000000 2:@0.338979:0.716872:0.347962:0.716872:0.347962:0.700438:0.338979:0.700438:0.000000 AC BC:@0.360294:0.709134:0.420026:0.709134:0.420026:0.692728:0.360294:0.692728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.382880:0.708579:0.398213:0.708579:0.398213:0.694863:0.382880:0.694863:0.000000 ) :@0.419971:0.709134:0.468198:0.709134:0.468198:0.692700:0.419971:0.692700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.428714:0.708579:0.444047:0.708579:0.444047:0.694863:0.428714:0.694863:0.000000 1:@0.451594:0.702893:0.460577:0.702893:0.460577:0.686459:0.451594:0.686459:0.000000 2:@0.451594:0.716872:0.460577:0.716872:0.460577:0.700438:0.451594:0.700438:0.000000 AB:@0.468124:0.709134:0.486771:0.709134:0.486771:0.692728:0.468124:0.692728:0.000000:0.000000 Así, :@0.073086:0.740947:0.101352:0.740947:0.101352:0.724514:0.073086:0.724514:0.000000:0.000000:0.000000:0.000000:0.000000 DE:@0.101286:0.740947:0.120853:0.740947:0.120853:0.724541:0.101286:0.724541:0.000000:0.000000 :@0.120798:0.740947:0.164301:0.740955:0.164301:0.724521:0.120798:0.724514:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.124792:0.740393:0.140125:0.740393:0.140125:0.726677:0.124792:0.726677:0.000000 1:@0.148104:0.733557:0.156270:0.733557:0.156270:0.718617:0.148104:0.718617:0.000000 2:@0.148104:0.746580:0.156270:0.746580:0.156270:0.731641:0.148104:0.731641:0.000000 AB:@0.164264:0.740955:0.182910:0.740955:0.182910:0.724549:0.164264:0.724549:0.000000:0.000000 prueba que los vectores son colineales y, en consecuencia, el segmento :@0.182855:0.740955:0.710783:0.740955:0.710783:0.724521:0.182855:0.724521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de recta , es paralelo al segmento de recta :@0.073093:0.757597:0.414336:0.757597:0.414336:0.741163:0.073093:0.741163:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.136156:0.758179:0.140242:0.758179:0.140242:0.740525:0.136156:0.740525:0.000000 D E:@0.140150:0.757597:0.166878:0.757597:0.166878:0.741191:0.140150:0.741191:0.000000:0.000000:0.000000 4:@0.166804:0.758179:0.170890:0.758179:0.170890:0.740525:0.166804:0.740525:0.000000 3:@0.414198:0.758179:0.418284:0.758179:0.418284:0.740525:0.414198:0.740525:0.000000 A, B:@0.418192:0.757597:0.443410:0.757597:0.443410:0.741191:0.418192:0.741191:0.000000:0.000000:0.000000:0.000000 4:@0.443355:0.758179:0.447441:0.758179:0.447441:0.740525:0.443355:0.740525:0.000000 , o sea, , || , . Adicionalmente :@0.447349:0.757597:0.710414:0.757597:0.710414:0.741163:0.447349:0.741163:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.499313:0.758179:0.503399:0.758179:0.503399:0.740525:0.499313:0.740525:0.000000 D E:@0.503307:0.757597:0.530034:0.757597:0.530034:0.741191:0.503307:0.741191:0.000000:0.000000:0.000000 4 3:@0.529961:0.758179:0.553761:0.758179:0.553761:0.740525:0.529961:0.740525:0.000000:0.000000:0.000000 A B:@0.553669:0.757597:0.579476:0.757597:0.579476:0.741191:0.553669:0.741191:0.000000:0.000000:0.000000 4:@0.579403:0.758179:0.583489:0.758179:0.583489:0.740525:0.579403:0.740525:0.000000 a este resultado, se obtiene el siguiente postulado: la longitud del segmento , es la :@0.073056:0.774239:0.710333:0.774239:0.710333:0.757805:0.073056:0.757805:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.634698:0.774821:0.638784:0.774821:0.638784:0.757167:0.634698:0.757167:0.000000 D E:@0.638711:0.774239:0.665788:0.774239:0.665788:0.757833:0.638711:0.757833:0.000000:0.000000:0.000000 4:@0.665733:0.774821:0.669819:0.774821:0.669819:0.757167:0.665733:0.757167:0.000000 mitad de la longitud del segmento , . Es decir que ІІ:@0.073074:0.795443:0.469290:0.795443:0.469290:0.779009:0.073074:0.779009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.329193:0.796026:0.333279:0.796026:0.333279:0.778371:0.329193:0.778371:0.000000 A B:@0.333187:0.795443:0.358902:0.795443:0.358902:0.779037:0.333187:0.779037:0.000000:0.000000:0.000000 4:@0.358828:0.796026:0.362915:0.796026:0.362915:0.778371:0.358828:0.778371:0.000000 DE:@0.469106:0.795443:0.488673:0.795443:0.488673:0.779037:0.469106:0.779037:0.000000:0.000000 ІІ ІІ:@0.488618:0.795443:0.547285:0.795442:0.547285:0.779008:0.488618:0.779009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.500178:0.794888:0.515511:0.794888:0.515511:0.781173:0.500178:0.781173:0.000000 1:@0.523061:0.789201:0.532044:0.789201:0.532044:0.772767:0.523061:0.772767:0.000000 2:@0.523061:0.803180:0.532044:0.803180:0.532044:0.786746:0.523061:0.786746:0.000000 AB:@0.547193:0.795442:0.565840:0.795442:0.565840:0.779036:0.547193:0.779036:0.000000:0.000000 ІІ.:@0.565785:0.795442:0.576608:0.795442:0.576608:0.779008:0.565785:0.779008:0.000000:0.000000:0.000000 3.2 Aplicación de vectores en la física:@0.073096:0.823816:0.362889:0.823816:0.362889:0.806869:0.073096:0.806869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 El ejemplo que consideramos es el de una persona que se moviliza en una silla de ruedas. :@0.073096:0.850471:0.710193:0.850471:0.710193:0.834037:0.073096:0.834037:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En la Figura 3.2. se muestra en forma esquemática este dispositivo y se asume que está :@0.073096:0.867113:0.710513:0.867113:0.710513:0.850679:0.073096:0.850679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.706482:0.867113:0.710513:0.867113:0.710513:0.850679:0.706482:0.850679:0.000000 ocupado por una persona. En una superficie horizontal seca, esta persona se moviliza sin :@0.073096:0.883755:0.710178:0.883755:0.710178:0.867321:0.073096:0.867321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 inconvenientes.:@0.073096:0.900396:0.187433:0.900396:0.187433:0.883963:0.073096:0.883963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Tema 3. Aplicación de los vectores geométricos:@0.073089:0.098522:0.769311:0.098522:0.769311:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿Cuáles son aplicaciones diferentes de los vectores en situaciones :@0.292999:0.174128:0.798558:0.174128:0.798558:0.157694:0.292999:0.157694:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cercanas a tu entorno?:@0.292999:0.190770:0.457761:0.190770:0.457761:0.174336:0.292999:0.174336:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Reto matemático:@0.302768:0.139600:0.437491:0.139600:0.437491:0.122653:0.302768:0.122653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Colineales.:@0.749029:0.414265:0.822876:0.412808:0.822350:0.397659:0.748503:0.399116:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Término :@0.822772:0.412810:0.883818:0.411605:0.883299:0.396670:0.822253:0.397875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que hace referencia :@0.749560:0.429388:0.883016:0.426755:0.882497:0.411820:0.749041:0.414454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a los puntos que se :@0.750086:0.444512:0.881178:0.441926:0.880659:0.426991:0.749567:0.429577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 encuentran en la misma :@0.750612:0.459636:0.913979:0.456413:0.913460:0.441478:0.750093:0.444701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 recta.:@0.751137:0.474760:0.786973:0.474053:0.786453:0.459118:0.750618:0.459825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 El punto medio de los :@0.751663:0.489884:0.900179:0.486953:0.899660:0.472019:0.751144:0.474949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lados de un triángulo :@0.752189:0.505007:0.896638:0.502157:0.896119:0.487222:0.751670:0.490073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 divide a cada lado en :@0.752715:0.520131:0.896125:0.517302:0.895606:0.502367:0.752195:0.505196:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dos de igual medida.:@0.753240:0.535255:0.891047:0.532536:0.890528:0.517601:0.752721:0.520320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Glosario:@0.802084:0.392432:0.867663:0.392432:0.867663:0.375485:0.802084:0.375485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Figura 3.1.:@0.796414:0.355002:0.869447:0.355002:0.869447:0.338568:0.796414:0.338568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.734802:0.334266:0.742889:0.334266:0.742889:0.320843:0.734802:0.320843:0.000000 B:@0.919703:0.334266:0.926932:0.334266:0.926932:0.320843:0.919703:0.320843:0.000000 E:@0.881283:0.295313:0.887925:0.295313:0.887925:0.281890:0.881283:0.281890:0.000000 D:@0.776026:0.295313:0.785453:0.295313:0.785453:0.281890:0.776026:0.281890:0.000000 C:@0.827306:0.260286:0.835409:0.260286:0.835409:0.246863:0.827306:0.246863:0.000000 AC:@0.793691:0.270997:0.809565:0.270997:0.809565:0.257574:0.793691:0.257574:0.000000:0.000000 BC:@0.849183:0.270647:0.864454:0.270647:0.864454:0.257224:0.849183:0.257224:0.000000:0.000000 DE:@0.816928:0.313889:0.832937:0.313889:0.832937:0.300466:0.816928:0.300466:0.000000:0.000000 T:@0.734802:0.297279:0.741443:0.297279:0.741443:0.283855:0.734802:0.283855:0.000000 Silla de ruedas:@0.767613:0.905062:0.840670:0.905062:0.840670:0.893667:0.767613:0.893667:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Figura 3.2.:@0.796412:0.932863:0.869445:0.932863:0.869445:0.916430:0.796412:0.916430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 DBA 5 (Ev. 1) Localiza objetos geométricos en el plano cartesiano:@0.075755:0.971366:0.417295:0.971366:0.417295:0.959414:0.075755:0.959414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@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