Question

For what value of $p$ are the points $(2,1),(p,-1)$ and $(-1,3)$ collinear.

Answer 1

${}^m{A}_C{=}^m{A}_B$

$\Rightarrow \frac{3-1}{-1-2}=\frac{-1-1}{P-2}$

$\Rightarrow \frac{-2}{3}=\frac{-2}{P-2}$

$\Rightarrow 3=P-2$

$\therefore P=5$

Hence the value of $P=5$.