Question

O valor de m, para que os pontos A (2m + 1, 2), B(-6, -5) e C(0, 1) sejam colineares, é:​

Answer 1

Utilizando o método do determinante, para que os pontos sejam contínuos, temos:

$\left|\begin{array}{ccc}x_A&y_A&1\\x_B&y_B&1\\x_C&y_C&1\end{array}\right|~=~0\\\\\\\\\left|\begin{array}{ccc}(2m+1)&2&1\\-6&-5&1\\0&1&1\end{array}\right|~=~0\\\\\\\\(~(2m+1).(-5).1+(-6).1.1+0.2.1~)~-~(~1.(-5).0+1.1.(2m+1)+1.2.(-6)~)~=~0\\\\\\(~-10m-5+(-6)+0~)~-~(~0+2m+1+(-12)~)~=~0\\\\\\(~-10m-5+-6~)~-~(~2m+1-12~)~=~0\\\\\\(-10m-11)~-~(2m-11)~=~0\\\\\\-10m-11-2m+11~=~0\\\\\\-12m~=~0\\\\\\\boxed{m~=~0}$