Question

Find the value of $k$ for which the points $A(-2,3),B(1,2)$ and $C(k,0)$ are collinear.

Answer 1

Given points $A(-2,3),B(1,2)$ and $C(k,0)$

points are collinear means

slope of $AB=$ slope of $BC$

$\frac{2-3}{1-(-2)}=\frac{0-2}{k+1}$

$\Rightarrow -1/3=-2/k+1$

$\Rightarrow -1(k+1)=-6$

$\Rightarrow -k+1=-6$

$\Rightarrow -k=-6-1$

$\Rightarrow +k=+7$

$\therefore k=7.$