Question

Using section formula, show that the points A(7, -5), B(9, -3) and C(13,1) are collinear.

Answer 1

use area of triangle=0

Answer 2

Hey dear,

◆ Proof-
Section formula states that points A, B & C are collinear if point C divides distance AB in some fixed ratio.

Let point C divide AB in ratio k:1,
For x-coordinates,
x = (kx1+x2)(k+1)
13 = (9k+7)/(k+1)
13k + 13 = 9k + 7
4k = -4
k = -1

For y-coordinates,
y = (ky1+y2)(k+1)
1 = (-3k-5)/(k+1)
k + 1 = -3k -5
4k = -4
k = -1

As point C divides AB in ratio -1:1, we can say that A, B & C are collinear.

Hope it helps...