Question

5) Dados os pontos P(2, 1), Q(5, 7) e R(k, − 9), determine o valor de k para que esses pontos
estejam alinhados.

Answer 1

$\begin{array}{l}\boxed{\text{Os\ pontos\ ( a,b) ,( c,d) ,( e,f) \ estão\ alinhados\ } \Leftrightarrow \begin{vmatrix}a & b & 1\\c & d & 1\\e & f & 1\end{vmatrix} =0}\\\\\therefore \begin{vmatrix}2 & 1 & 1\\5 & 7 & 1\\k & -9 & 1\end{vmatrix} =0\\\\\Longrightarrow 14-45+k-( 7k+5-18) =0\\\\\Longrightarrow -6k-18=0\\\\\Longrightarrow 6k=-18\\\\\Longrightarrow \boxed{\boxed{k=-3}}\end{array}$