Question

5-0 ponto M(5, 1/2) é o ponto médio do segmento de origem A(3, -1). Determine as coordenadas da outra extremidade do segmento.​

Answer 1

O ponto médio M é dado por:

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

Vamos então achar as coordenadas da outra extremidade do segmento, o ponto B:

$\sf \left(5~,~\dfrac{1}{2}\right)~=~\left(\dfrac{3~+~x_B}{2}~,~\dfrac{-1~+~y_B}{2}\right)~~~\longrightarrow~\left\{\begin{array}{ccc}\sf 5&\sf =&\sf \dfrac{3~+~x_B}{2}\\\\\sf \dfrac{1}{2}&\sf =&\sf \dfrac{-1~+~y_B}{2}\end{array}\right.$

Resolvendo as duas equações:

$\sf 5~=~\dfrac{3~+~x_B}{2}\\\\\\\sf 2\cdot 5~=~3~+~x_B\\\\\\10~=~3~+~x_B\\\\\\x_B~=~10~-~3\\\\\\\boxed{\sf x_B~=~7}\\\\\\\\\sf \dfrac{1}{2}~=~\dfrac{-1~+~y_B}{2}\\\\\\\sf 2\cdot \dfrac{1}{2}~=\,-1~+~y_B\\\\\\1~=\,-1~+~y_B\\\\\\y_B~=~1~+~1\\\\\\\boxed{\sf y_B~=~2}$

$\Huge{\begin{array}{c}\Delta \tt{\!\!\!\!\!\!\,\,o}\!\!\!\!\!\!\!\!\:\,\perp\end{array}}Qualquer~d\acute{u}vida,~deixe~ um~coment\acute{a}rio$