Question

Considere em um plano três pontos colineares A(2k;0)B(1;-4) e C(6; 4)Diante disso calcule o valor de k.

Answer 1

$\begin{array}{l}\boxed{\text{Os\ pontos\ ( a,b) ,( c,d) ,( e,f) \ são\ colinerares} \Leftrightarrow \begin{vmatrix}a & b & 1\\c & d & 1\\e & f & 1\end{vmatrix} =0}\\\\\therefore \begin{vmatrix}2k & 0 & 1\\1 & -4 & 1\\6 & 4 & 1\end{vmatrix} =0\\\\\Longrightarrow -8k+4-( -24+8k) =0\ \ \ \ \ (\text{Regra\ de\ Sarrus})\\\\\Longrightarrow -16k+28=0\\\\\Longrightarrow 16k=28\\\\\Longrightarrow \boxed{\boxed{k=\frac{7}{4}}}\end{array}$