<Text-field style="Heading 1" layout="Heading 1">Introdu\303\247\303\243o</Text-field>

<Text-field style="Heading 1" layout="Heading 1">Mediatriz Perpendicular de um Segmento de Reta</Text-field>

Dado um segmento de reta determinado por dois pontos no plano, obter a equa\303\247\303\243o da mediatriz perpendicular do segmento de reta.

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Tabela 1 ilustra como encontrar a equa\303\247\303\243o da mediatriz perpendicular do segmento determinado pelos pontos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNictSSNtbkdGJDYkUSIyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjg2LVEqJnVtaW51czA7RidGNEY7L0Y/Rj1GQUZDRkVGR0ZJL0ZMUSwwLjIyMjIyMjJlbUYnL0ZPRlYtRjE2JFEiNUYnRjRGNEY0RjQ= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtbkdGJDYkUSI3RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JFEiMUYnRjRGNEY0RjQ=. A abordagem incorpora os passos de mat\303\241mtica direta encontrando o ponto m\303\251dio e a inclina\303\247\303\243o do segmento de reta, e construindo a equa\303\247\303\243o da mediatriz perpendicular atrav\303\251s da forma ponto-inclina\303\247\303\243o da reta.

Obter o ponto m\303\251dio do segmento.

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print(); # input placeholder

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Obter a inclina\303\247\303\243o do segmento.

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print(); # input placeholder

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Utilize a forma ponto-inclina\303\247\303\243o da reta com inclina\303\247\303\243o tomado como a rec\303\255proca negativa da inclina\303\247\303\243o do segmento, e o ponto como o ponto m\303\251dio do segmento.

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print(); # input placeholder

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Tabela 1 C\303\241lculo da equa\303\247\303\243o da bissetriz perpendicular de um segmento de reta

Tabela 2 implementa o c\303\241lculo com ferramentas do pacote Student Precalculus.

Tools\342\211\273Load Package: Student Precalculus

Loading Student:-Precalculus

with(Student:-Precalculus):

Entre com o primeiro ponto. Menu de Contexto: Associe Nome

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Entre com o segundo ponto. Menu de Contexto: Associe Nome

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Obtenha a equa\303\247\303\243o da bissetriz perpendicular com o comando Line . Note o uso dos comandos Slope and Midpoint.

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print(); # input placeholder

L0kieUc2IiwmSSJ4R0YkIyEiJiIiJyMiIigiIiUiIiI=

Tabela 2 Bissetriz perpendicular atrav\303\251s dos comandos Slope, Midpoint, e Line de Student Precalculus

Tabela 3 mostra como obter a equa\303\247\303\243o da mediatriz perpendicular com as ferramentas do pacote geometry. H\303\241 um pouco de sobrecarga neste pacote, mas os comandos dispon\303\255veis s\303\243o robustos e eficazes. Se os nomes das vari\303\241veis associadas com os eixos horizontal e vertical n\303\243o s\303\243o explicitamente declaradas, ent\303\243o, uma janela pop-up ir\303\241 solicitar essa informa\303\247\303\243o quando o comando Equation \303\251 usado para extrair a equa\303\247\303\243o da mediatriz perpendicular.

Chame o pacote geometry.

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Declare ao pacote os nomes associados com os eixos horizontal e vertical.

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print(); # input placeholder

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Defina os dois pontos como objetos no pacote.

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Extrair a equa\303\247\303\243o da mediatriz perpendicular.

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print(); # input placeholder

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isolate( , y );

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Tabela 3 O uso do pacote geometry obt\303\251m a mediatriz perpendicular de um segmento de reta

\303\211 lament\303\241vel que as estruturas de dados para pontos e linhas de n\303\255vel superior e no pacote Precalculus n\303\243o s\303\243o compat\303\255veis com esses no pacote geometry. Essencialmente, isso significa que os c\303\241lculos dentro do pacote geometry s\303\243o isolados a partir de muitas das funcionalidades de n\303\255vel superior do Maple, e vice-versa.

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<Text-field style="Heading 1" layout="Heading 1">Desenhe uma Perpendicular para uma Reta</Text-field>

Dada uma linha no plano, e um ponto n\303\243o pertencente \303\240 reta, obter a equa\303\247\303\243o da reta que passa pelo ponto dado e est\303\241 perpendicular \303\240 reta dada.

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Tabela 4 ilustra como usar a funcionalidade de n\303\255vel superior para desenhar uma perpendicular do ponto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNictSSNtb0dGJDYtUSomdW1pbnVzMDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGOS8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y5LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGSC1JI21uR0YkNiRRIjFGJ0Y0LUYxNi1RIixGJ0Y0RjcvRjtRJXRydWVGJ0Y8Rj5GQEZCRkQvRkdRJjAuMGVtRicvRkpRLDAuMzMzMzMzM2VtRictRkw2JFEiN0YnRjRGNEY0RjQ= para a linha 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

Entre com a equa\303\247\303\243o da reta dada. Pressione a tecla Enter.

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print(); # input placeholder

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isolate( , y );

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Usando a forma ponto-inclina\303\247\303\243o da reta, escreva a equa\303\247\303\243o da reta que passa pelo ponto dado e tendo como sua inclina\303\247\303\243o, a rec\303\255proca negativa da inclina\303\247\303\243o da reta dada.

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print(); # input placeholder

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Usando r\303\263tulos de equa\303\247\303\243o, forme uma seq\303\274\303\252ncia da reta dada e sua perpendicular. Pressione a tecla Enter.

Menu de Contexto: Plots\342\211\273Plot Builder Definir os intervalos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSI4RidGLy1GLDYtUSYmbGVxO0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yNzc3Nzc4ZW1GJy9GRUZOLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0ZKLUZHNiRRIjBGJ0YvLUYsNi1RIixGJ0YvRjIvRjZGVkY3RjlGO0Y9Rj8vRkJRJjAuMGVtRicvRkVRLDAuMzMzMzMzM2VtRidGWUZKLUZRNiVRInlGJ0ZURldGSkZGRi8= Op\303\247\303\265es: Cor da reta dada: preta; a da perpendicular, vermelha Adicione um t\303\255tulo

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print(); # input placeholder

NiQvLCZJInhHNiIiIiNJInlHRiYiIiQiIiovRigsJkYlI0YpRicjIiM8RiciIiI=

LUkjbW9HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2LlEnJnJhcnI7RicvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHUSV0cnVlRicvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkQ=

plots[:-display](plots[:-implicitplot](2*x+3*y = 9, x = -8 .. 0, y = 0 .. 8, color = "Black"), plots[:-implicitplot](y = 3/2*x+19/2, x = -8 .. 0, y = 0 .. 8), scaling = constrained, caption = "Figure 1");

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Uma figura mais satisfat\303\263ria pode ser desenhada se primeiro for calculada a interse\303\247\303\243o entre a reta dada e sua perpendicular.

Usando r\303\263tulos de equa\303\247\303\243o, forme uma seq\303\274\303\252ncia das equa\303\247\303\265es da reta dada e sua perpendicular. Pressione a tecla Enter.

Menu de Contexto: Solve\342\211\273Solve

Usando o modelo de avalia\303\247\303\243o a partir da paleta Expression, converter a solu\303\247\303\243o para uma lista que representa um ponto de n\303\255vel superior no Maple. Pressione a tecla Enter.

NiQvLCZJInhHNiIiIiNJInlHRiYiIiQiIiovRigsJkYlI0YpRicjIiM8RiciIiI=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NiQvLCZJInhHNiIiIiNJInlHRiYiIiQiIiovRigsJkYlI0YpRicjIiM8RiciIiI=

solve( { } );

PCQvSSJ4RzYiIyEjTCIjOC9JInlHRiUjIiNoRig=

LUklZXZhbEclKnByb3RlY3RlZEc2JDckSSJ4RzYiSSJ5R0YoPCQvRicjISNMIiM4L0YpIyIjaEYu

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQjISNMIiM4IyIjaEYl

Tools\342\211\273Load Package: Gr\303\241ficos

Carregar plots

with(plots):

Criar gr\303\241ficos separados do ponto dado e o ponto de interse\303\247\303\243o da reta dada e sua perpendicular.

Criar um gr\303\241fico do segmento de reta ligando estes dois pontos.

Criar um gr\303\241fico da reta dada.

Mesclar os tr\303\252s gr\303\241ficos na Figura 2.

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LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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Tabela 4 Utilizar funcionalidades de n\303\255vel superior para desenhar uma perpendicular de um ponto para uma reta

JSFH

Figura 2 tamb\303\251m poderia ser criada interativamente utilizando o Plot Builder acessado a partir do Menu de Contexto, mas isso implicaria componentes de arrastar e largar sobre o gr\303\241fico final. \303\211 mais dif\303\255cil descrever estas opera\303\247\303\265es do que execut\303\241-las, por isso optamos pela constru\303\247\303\243o baseada em comandos da figura.

Tabela 5 mostra como os c\303\241lculos da Tabela 4 podem ser implementados usando ferramentas do pacote Student Precalculus. N\303\243o \303\251 necess\303\241rio reinstalar este pacote se isto tiver sido feito uma vez na sess\303\243o, mas por uma quest\303\243o de rigor esta etapa \303\251 repetida.

Tools\342\211\273Load Package: Student Precalculus

with(Student:-Calculus1):

Carregar Student:-Precalculus

with(Student:-Precalculus):

Arraste-solte (copiar/colar ou digitar) a equa\303\247\303\243o da reta dada.

LywmSSJ4RzYiIiIjSSJ5R0YlIiIkIiIq

isolate( , y );

L0kieUc2IiwmIiIkIiIiSSJ4R0YkIyEiI0Ym

Fornecimento para comando Line a rec\303\255proca negativa da inclina\303\247\303\243o da reta dada e o ponto do qual a perpendicular est\303\241 para ser desenhada.

Ji1JJUxpbmVHNiI2JCMiIiQiIiM3JCEiIiIiKDYjIiIi

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print(); # input placeholder

L0kieUc2IiwmSSJ4R0YkIyIiJCIiIyMiIzxGKSIiIg==

Tabela 5 Usando o pacote Student Precalculus para desenhar uma perpendicular de um ponto a uma reta

Tabela 6 mostra como os c\303\241lculos da Tabela 4 pode ser implementados no pacote geometry. N\303\243o \303\251 necess\303\241rio reinstalar este pacote ou declarar novamente as vari\303\241veis associadas com os eixos horizontal e vertical, se isto tiver sido feito uma vez na sess\303\243o, mas por uma quest\303\243o de rigor, essas etapas s\303\243o repetidas.

Instale o pacote geometry.

Declare os nomes das vari\303\241veis associadas com os eixos horizontal e vertical.

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QyQ+STNfRW52SG9yaXpvbnRhbE5hbWVHNiJJInhHRiUhIiI=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

QyQ+STFfRW52VmVydGljYWxOYW1lRzYiSSJ5R0YlISIi

Defina o ponto e a reta dada, como objetos no pacote geometry.

QyYtSSZwb2ludEc2IjYlSSJDR0YlISIiIiIoRigtSSVsaW5lR0YlNiVJIlJHRiUvLCZJInhHRiUiIiNJInlHRiUiIiQiIio3JEYwRjJGKA==

Defina a perpendicular que passa pelo ponto dado e obtenha a sua equa\303\247\303\243o.

Menu de Contexto: Solve\342\211\273Isolate Expression for\342\211\273LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= (Esta reescrita da equa\303\247\303\243o \303\251 simplesmente para facilitar a compara\303\247\303\243o com o resultado na Tabela 4).

QyUtSTJQZXJwZW5kaWN1bGFyTGluZUc2IjYlSSNDUkdGJUkiQ0c9RiVJJmZhbHNlRyUqcHJvdGVjdGVkR0VcW2wjSS5nZW9tMmQvY29vcmRzR0YlNyQhIiIiIihJLGdlb20yZC9mb3JtR0YlSShwb2ludDJkR0YlSSJSRz1GJUYqRVxbbCVGMUknbGluZTJkR0YlSS5nZW9tMmQvY29lZmZzR0YlNygiIiFGOUY5IiIjIiIkISIqSTRnZW9tMmQvVmVydGljYWxOYW1lR0YlSSJ5R0YlSTZnZW9tMmQvSG9yaXpvbnRhbE5hbWVHRiVJInhHRiVGLy1JKUVxdWF0aW9uR0YlNiNGJw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LywoIiM8IiIiSSJ4RzYiIiIkSSJ5R0YnISIjIiIh

isolate( , y );

L0kieUc2IiwmSSJ4R0YkIyIiJCIiIyMiIzxGKSIiIg==

Obter as coordenadas do ponto de interse\303\247\303\243o da reta dada e a perpendicular. (Isso \303\251 para facilitar o desenho de uma figura semelhante \303\240 Figura 2).

QyUtSS1pbnRlcnNlY3Rpb25HNiI2JUkiRUdGJUkiUkc9RiVJJmZhbHNlRyUqcHJvdGVjdGVkR0VcW2wlSSxnZW9tMmQvZm9ybUdGJUknbGluZTJkR0YlSS5nZW9tMmQvY29lZmZzR0YlNygiIiFGMUYxIiIjIiIkISIqSTRnZW9tMmQvVmVydGljYWxOYW1lR0YlSSJ5R0YlSTZnZW9tMmQvSG9yaXpvbnRhbE5hbWVHRiVJInhHRiVJI0NSRz1GJUYqRVxbbCVGLUYuRi83KEYxRjFGMUYzISIjIiM8RjVGNkY3RjghIiItSSxjb29yZGluYXRlc0dGJTYjRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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Definir o segmento de reta que liga o ponto dado e o ponto de interse\303\247\303\243o da reta dada e sua perpendicular.

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JSFH

Use o comando draw no pacote geometry para desenhar os objetos do pacote, nomeadamente, a reta dada, o segmento de reta LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== e os pontos C e ELUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEiLkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRi8=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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Tabela 6 Usando o pacote geometry para desenhar uma perpendicular de um ponto a uma reta

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Embora o paradigma para a nomea\303\247\303\243o no pacote geometry n\303\243o \303\251 a norma para o Maple, o pacote fornece muitos comandos \303\272teis para o trabalho em geometria anal\303\255tica. Em particular, o comando draw \303\251 \303\272til porque ele desenhar\303\241 os objetos do pacote, objetos que os comandos de gr\303\241fico ordin\303\241rio no Maple n\303\243o s\303\243o projetados aos gr\303\241fico. Note tamb\303\251m como as coordenadas de um ponto de interse\303\247\303\243o de duas retas \303\251 retornada como uma lista, ao contr\303\241rio do retorno do comando solve de n\303\255vel superior . S\303\243o estes pequenos detalhes que determinam o qu\303\243o f\303\241cil um c\303\241lculo ser\303\241 implementado de uma particular pe\303\247a de software.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 1" layout="Heading 1">Dist\303\242ncia de um Ponto a uma Reta</Text-field>

Calcule a dist\303\242ncia de um ponto a uma reta.

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Embora a dist\303\242ncia do ponto 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 para a linha LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJ4RidGL0YyLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GVi1GLDYlUSJiRidGL0YyRjUtRiw2JVEieUYnRi9GMkZSLUYsNiVRImNGJ0YvRjItRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yNzc3Nzc4ZW1GJy9GTkZfby1JI21uR0YkNiRRIjBGJ0Y5Rjk= \303\251 dada pela f\303\263rmula

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vamos calcular a dist\303\242ncia do ponto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNictSSNtb0dGJDYtUSomdW1pbnVzMDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGOS8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y5LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGSC1JI21uR0YkNiRRIjFGJ0Y0LUYxNi1RIixGJ0Y0RjcvRjtRJXRydWVGJ0Y8Rj5GQEZCRkQvRkdRJjAuMGVtRicvRkpRLDAuMzMzMzMzM2VtRictRkw2JFEiN0YnRjRGNEY0RjQ= a partir da reta LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUYzNi1RIitGJ0YvRjZGOUY7Rj1GP0ZBRkMvRkZRLDAuMjIyMjIyMmVtRicvRklGVy1GLDYkUSIzRidGL0YyLUZLNiVRInlGJ0ZORlEtRjM2LVEiPUYnRi9GNkY5RjtGPUY/RkFGQy9GRlEsMC4yNzc3Nzc4ZW1GJy9GSUZdby1GLDYkUSI5RidGL0Yv dos primeiros princ\303\255pios. Por isso, precisamos desenhar uma perpendicular de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNictSSNtb0dGJDYtUSomdW1pbnVzMDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGOS8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y5LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGSC1JI21uR0YkNiRRIjFGJ0Y0LUYxNi1RIixGJ0Y0RjcvRjtRJXRydWVGJ0Y8Rj5GQEZCRkQvRkdRJjAuMGVtRicvRkpRLDAuMzMzMzMzM2VtRictRkw2JFEiN0YnRjRGNEY0RjQ= para a reta, obtenha as coordenadas do ponto de interse\303\247\303\243o da reta dada com esta perpendicular, e calcular a dist\303\242ncia a partir esses dois pontos.

Na Tabela 4, o ponto de interse\303\247\303\243o da perpendicular de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNictSSNtb0dGJDYtUSomdW1pbnVzMDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGOS8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y5LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGSC1JI21uR0YkNiRRIjFGJ0Y0LUYxNi1RIixGJ0Y0RjcvRjtRJXRydWVGJ0Y8Rj5GQEZCRkQvRkdRJjAuMGVtRicvRkpRLDAuMzMzMzMzM2VtRictRkw2JFEiN0YnRjRGNEY0RjQ= para a reta dada \303\251 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 . Assim, a dist\303\242ncia LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== \303\251 dada por

LUklc3FydEc2IjYjLCYqJC1JIitHJSpwcm90ZWN0ZWRHNiQhIiIjIiNMIiM4IiIjIiIiKiQtRik2JCIiKCMhI2hGL0YwRjE=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCQqJCIjOCMiIiIiIiMjIiM1RiQ=

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Como uma checagem, a f\303\263rmula de dist\303\242ncia tamb\303\251m d\303\241

KiYtSSRhYnNHJSpwcm90ZWN0ZWRHNiMsKC1JIipHRiU2JCIiIyEiIiIiIi1GKTYkIiIkIiIoRi0hIipGLUYtLUklc3FydEc2JEYlSShfc3lzbGliRzYiNiMsJi1JIl5HRiU2JEYrRitGLS1GOzYkRjBGK0YtRiw=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCQqJCIjOCMiIiIiIiMjIiM1RiQ=

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O comando Distance no pacote Precalculus d\303\241

LUkpRGlzdGFuY2VHNiI2JDckISIiIiIoNyQjISNMIiM4IyIjaEYs

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCQqJCIjOCMiIiIiIiMjIiM1RiQ=

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e (usando Tabela 6) o comando distance no pacote geometry d\303\241

LUkpZGlzdGFuY2VHNiI2JEkiQ0c9RiRJJmZhbHNlRyUqcHJvdGVjdGVkR0VcW2wjSS5nZW9tMmQvY29vcmRzR0YkNyQhIiIiIihJLGdlb20yZC9mb3JtR0YkSShwb2ludDJkR0YkSSJFRz1GJEYoRVxbbCNGKzckIyEjTCIjOCMiI2hGN0YvRjA=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCQqJiIkKyIjIiIiIiIjIiM4RiUjRiZGKA==

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que, naturalmente, simplifica a 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.JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=