Question

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

Answer 1

A, B and C could only be collinear if the slopes of two line segments connecting the three lines, are same:

let m1 be the slope of line segment b/w (7,-5) and (9,-3)

..... m2 be the slope of line segment b/w (9,-3) and (13,1)

m = y2 - y1 / x2 - x1

m1 = -3 - (-5) / 9 - 7
= 2 / 2
= 1

m2 = 1 - (-3) / 13 - 9
= 4 / 4
= 1

since m1 is equal to m2

the points A, B and C are collinear