Question

If points A(-2,1), B(a,b), and C(4,-1) are colllinear and a-b=1. Find the values of a and b.

Answer 1

The points (-2,1) ,(a,b) and ( 4,-1) are collinear. Therefore, (x1(y2-y3) + x2(y3-y1) +x3(y1-y2) ) =0 also given : a-b=1 -2(b+1) + a(-1-1) + 4(1-b) =0 -2b-2 -2a +4 -4b =0 -6b-2a+2 =0 -6b-2a =-2 6b + 2a= 2 a +3b =1 also a-b =1 Subtract both equations, 4b=0 b=0 and a= 1 therefore B (1,0)