Question

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

Answer 1

$(2,1)$, $(p,-1)$ & $(-1,3)$ are collinear

$\Rightarrow \frac{-1-1}{p-2}=\frac{3-(-1)}{-1-p}$

$\Rightarrow \frac{-2}{p-2}=\frac{4}{-1-p}$

$\Rightarrow 2(1+p)=4(p-2)\Rightarrow 2+2p=4p-8$

$\Rightarrow 10-2p$ $\therefore$ $p=5$