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 Clearly, AC = AB + BC

`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`

Hence, A, B, C are collinear points.