Using distance formula, examine whether the following sets of points are collinear?

(- 1, 2), (5, 0), (2, 1)

Given points are A(- 1, 2), B(5, 0) and C(2, 1).

We need to check whether these points are collinear.

We know that for three points A, B and C to be collinear, the criteria to be satisfied is a linear relationship between AB, BC and AC.

Let us find the distances first,

We know that distance between two points (x₁, y₁) and (x₂, y₂) is

⇒ AC = √10 ..... (1)

⇒ AB = 2√10 ..... (2)

⇒ BC = √10 ..... (3)

From (1), (2), (3) we can see that AC + BC = AB.

∴ The three points are collinear.