Question

Find the value of $K$ if $(-3,11)$ , $(6,2)$ and $(K,4)$ are collinear points.

Answer 1

Let $A\equiv \underset{x_1{y}_1}{(-3,11)}$, $B\equiv \underset{x_2{y}_2}{(6,2)}$ and $C\equiv \underset{x_3{y}_3}{(K,4)}$.
Slope of line $AB=$ Slope of line $BC$
$\frac{y_2-y_1}{x_2-x_1}=\frac{y_3-y_2}{x_3-x_2}$
$\frac{2-11}{6+3}=\frac{4-2}{K-6}$
$\Rightarrow \frac{-9}{9}=\frac{2}{K-6}$
$\Rightarrow -1(K-6)=2$
$\Rightarrow -K+6=2$
$\Rightarrow -K=2-6$
$\Rightarrow -K=-4$
$\Rightarrow K=4$