Question

as coordenadas do ponto médio de um segmento AB são (1,-2). Sabendo-se que as coordenadas do ponto A são (2,5), então determine as coordenadas de B.

Answer 1

Resposta: B = (0 , -9)

O ponto médio é calculado por:

$\sf \left(x_M~,~y_M\right)~=~\left(\dfrac{x_A~+~x_B}{2}~,~\dfrac{y_A~+~y_B}{2}\right)$

Suubstituindo os valores:

$\sf \left(1~,\,-2\right)~=~\left(\dfrac{2~+~x_B}{2}~,~\dfrac{5~+~y_B}{2}\right)$

Com isso, tiramos duas equações:

$\boxed{\sf 1~=~\dfrac{2~+~x_B}{2}}~~~~~~\boxed{\sf -2~=~\dfrac{5~+~y_B}{2}}$

Calculando as coordenadas x e y do ponto B:

$\sf 1~=~\dfrac{2~+~x_B}{2}\\\\\\2\cdot 1~=~2~+~x_B\\\\\\x_B~=~2~-~2\\\\\\\boxed{\sf x_B~=~0}\\\\\\ -2~=~\dfrac{5~+~y_B}{2}\\\\\\2\cdot (-2)~=~5~+~y_B\\\\\\y_B~=\,-4~-~5\\\\\\\boxed{\sf y_B~=\,-9}$

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