Question

As coordenadas de ponto médio de um segmento AB são (-1;2). Sabendo-se:que as coordenadas do ponto A são
(2;5), calcule as coordenadas do ponto B .

Answer 1

As coordenadas do ponto B são (-4, -1).

• Resolvendo o problema

As coordenadas do ponto médio (M) são dadas pela média das coordenadas dos pontos A e B. Logo, usando os dados do enunciado, temos

$A(2,5)\\B(x_B,y_B)\\M(-1,2)$

$x_M=\dfrac{x_A+x_B}{2}\\\\\\-1=\dfrac{2+x_B}{2}\\\\\\2+x_B=-1\;.\;2\\\\\\2+x_B=-2\\\\\\x_B=-2-2\\\\\\\boxed{x_B=-4}$

$y_M=\dfrac{y_A+y_B}{2}\\\\\\2=\dfrac{5+y_B}{2}\\\\\\5+y_B=2\;.\;2\\\\\\5+y_B=4\\\\\\y_B=4-5\\\\\\\boxed{y_B=-1}$

• Conclusão

Portanto, as coordenadas do ponto B são (-4, -1).

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