Question

determine o valor de x para que os pponts sejam colineares a(-3,-11) b(0,-2) e c(×,13)

Answer 1

Para que 3 pontos sejam colineares (alinhados), o determinante da matriz formada por estes pontos deve valer 0, acompanhe:

$\left|\begin{array}{ccc}x_a&y_a&1\\x_b&y_b&1\\x_c&y_c&1\end{array}\right|~=~0\\\\\\\\\left|\begin{array}{ccc}-3&-11&1\\0&-2&1\\x&13&1\end{array}\right|~=~0$

$\left(~(-3).(-2).1+0.13.1+x.(-11).1~\right)~-~\left(~1.(-2).x+1.13.(-3)+1.(-11).0~\right)~=~0$

$\left(~6+0-11x~\right)~-~\left(~-2x-39+0~\right)~=~0\\\\\\6-11x+2x+39~=~0\\\\\\-9x+45~=~0\\\\\\9x~=~45\\\\\\x~=~\frac{45}{9}\\\\\\\boxed{x~=~5}$