Question

Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.

Answer 1

Let A (1 , -1) , B (5 , 2) and C (9 , 5) be the given points. Then, We have

AB = $\sqrt{{(5-1)}^2+{(2+1)}^2}$ = $\sqrt{16+9}$ = 5

BC = $\sqrt{{(5-9)}^2+{(2-5)}^2}$ = $\sqrt{16+9}$ = 5

and , AC = $\sqrt{{(1-9)}^2+{(-1-5)}^2}$ = $\sqrt{64+36}$ = 10

Clearly, AC = AB + BC

Hence A, B, C are collinear points