Question

If the (-1,-2),(p,q) and (4,0) are collinear ,then prove that 2p-5q=8

Answer 1

Since the given points are collinear,
Therefore,
Z
X1 (Y2 - Y3) +X2 (Y3 - Y1) + X3 (Y1 - Y2) =0
-1 (q - 0) + p (0 + 2) + 4(-2 - q) =0
-1(q) +p(2) +4(-2-q)=0
-q + 2p - 8 - 4q=0
2p - 5q=8.
Hence proved