Question

na figura abaixo os pontos A, B e C sao colineares .determine o valor da ordenada Y do ponto C mim ajuda por favor ​

Answer 1

A = (0 , -2)

B = (-3 , 0)

C = (-6 , y)

Se os pontos são colineares, o determinante formado pelos 3 pontos (como mostrado abaixo) deve valer 0 (zero), logo:

$\left|\begin{array}{ccc}x_A&y_A&1\\x_B&y_B&1\\x_C&x_y&1\end{array}\right|~=~0\\\\\\\left|\begin{array}{ccc}0&-2&1\\-3&0&1\\-6&y&1\end{array}\right|~=~0\\\\\\(~0.0.1+(-3).y.1+(-6).(-2).1~)~-~(~1.0.(-6)+1.y.0+1.(-2).(-3)~)~=~0\\\\\\(~0-3y+12~)~-~(~0+0+6~)~=~0\\\\\\(~-3y+12~)~-~(~6~)~=~0\\\\\\-3y+12-6~=~0\\\\\\-3y~=~-6\\\\\\y~=~\frac{-6}{-3}\\\\\\\boxed{y~=~2}$