Question

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

Answer 1

Let P(1, –1), Q(5, 2) and R(9, 5) be the given points. Then

PQ = \(\sqrt{(5-1)^2+(2+1)^2}\) = \(\sqrt{16+9}\) = \(\sqrt{25}\) = 5

QR = \(\sqrt{(9-5)^2+(5-2)^2}\) = \(\sqrt{16+9}\) = \(\sqrt{25}\) = 5

PR = \(\sqrt{(9-1)^2+(5+1)^2}\) = \(\sqrt{64+36}\) = \(\sqrt{100}\) = 10

⇒ PQ + QR = PR 

⇒ P, Q, R are collinear points.