Question

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

Answer 1

Three given point are collinear.

The given point are (2,1),(p,-1),(-1,3).

Three given point are collinear if

$y_1(x_2-x_3)+y_2(x_3-x_1)+y_3(x_1-x_2)=0$

$\Rightarrow 1(p+1)+(-1)(-1-2)+\left(3\right)(2-p)=0$

$\Rightarrow p+1+3+6-3p=0$

$\Rightarrow 2p=10$

$\Rightarrow p=\frac{10}{2}=5$