Question

Find the relation between x and y if the points A(x, y), B(-5, 7) and C (- 4,5) are collinear.​

Answer 1

Answer:

If A, B, C are collinear then area of triangle ABC = 0.

Area of triangle = 1/2 [(x1(y2-y3)+x2(y3-y1)+x3(y1-y2)] where x1,x2,x3,y1,y2,y3 are coordinates of A,B,C.

= 1/2 |(x(7 - 5) - 5(5 - y) -4(y - 7)| = 0

=> 2x - 25 + 5y - 4y + 28 = 0

∴ 2x + y + 3 = 0