Find the value of k if the points A(8,1),B(3,-4) and C(2,k) are collinear.

Explanation

These three points will be collinear if area of triangle `ABC` is `0`.

Area of a triangle can be given as,

`A = 1/2[x_1(y_2-y_3)+x_2(y_3-y_2)+x_3(y_1-y_2)]`

`1/2[8(-4-k)+3(k-1)+2(1+4)] = 0`

`=>-32-8k+3k-3+10 = 0`

`=>-5k =25=>k =-5`

So, for `k =-5`, these three points will be collinear.