Question

Find the value of ${}^{\prime }{p}^{\prime }$ for which the points $A(-5,1)$, $B(1,p)$ and $C(4,-2)$ are collinear.

Answer 1

Consider the given points.

$A(-5,1),B(1,p),C(4,-2)$

If the given points are collinear, then these points cannot be vertices of any triangles.

So, the area of triangle will be zero.

Therefore,

$\Delta =\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]=0$

$-5(p+2)+1(-2-1)+4(1-p)=0$

$-5p-10-3+4-4p=0$

$-9p-9=0$

$-9p=9$

$p=-1$

Hence, the value of $p$ is $-1$.