Question

A reta s passa por A(2,-1) e pelo ponto médio de \bar{BC} sendo B(0,-1) e C(-3,2).

A equação geral de s é dada por s:

(Escreva a equação no formato ax+by+c=0)

Answer 1

$\boxed{\begin{array}{l}\underline{\rm C\acute alculo~do~ponto~m\acute edio}\\\underline{\rm~de~\overline{\sf BC}}\\\sf x_M=\dfrac{0-3}{2}=-\dfrac{3}{2}\\\sf y_M=\dfrac{-1+2}{2}=\dfrac{1}{2}\\\sf M\bigg(-\dfrac{3}{2},\dfrac{1}{2}\bigg)\end{array}}$

$\boxed{\begin{array}{l}\begin{vmatrix}\sf2&\sf-1&\sf1\\\\\sf-\dfrac{3}{2}&\sf\dfrac{1}{2}&\sf1\\\\\sf x&\sf y&\sf1\end{vmatrix}=0\\\sf2\cdot\bigg(\dfrac{1}{2}-y\bigg)+1\cdot\bigg(-\dfrac{3}{2}-x\bigg)+1\cdot\bigg(-\dfrac{3}{2}y-\dfrac{1}{2}x\bigg)=0\\\sf 1-2y-\dfrac{3}{2}-x-\dfrac{3}{2}y-\dfrac{1}{2}x=0\cdot(2)\\\sf2-4y-3-2x-3y-x=0\\\sf -3x-7y-1=0\cdot(-1)\\\sf 3x+7y+1=0\end{array}}$