Question

quais são os possiveis valores de W para que os pontos (W,0); (-5,2) e (0,-3) estejam alinhados

Answer 1

Se 3 pontos são colineares, então o determinante da matriz formada por estes pontos (ver abaixo) deve valer 0.

$\left|\begin{array}{ccc}x_A&y_A&1\\x_B&y_B&1\\x_C&y_C&1\end{array}\right|~=~0\\\\\\\left|\begin{array}{ccc}w&0&1\\-5&2&1\\0&-3&1\end{array}\right|~=~0\\\\\\(~w.2.1+(-5).(-3).1+0.0.1~)~-~(~1.2.0+1.(-3).w+1.0.(-5)~)~=~0\\\\\\(~2w+15+0~)~-~(~0-3w+0~)~=~0\\\\\\2w+15+3w~=~0\\\\\\5w~=~-15\\\\\\w~=~\frac{-15}{5}\\\\\\\boxed{w~=~-3}$