Question

Find the value of p for which the points (-1,3) , (2,p) and (5,-1) are collinear.

Answer 1

Let A( -1 , 3 ), B( 2 , p) and C( 5 , - 1 ) be 3 collinear points.
Then Area ABC = 0
Then,[-1(p+1)+2(-1-3)+5(3-p)]=0 [1]
i.e. -p-1-8+15-5p=0 i.e. 6=6p
p=1