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

(1, 5), (2, 3), (- 2, - 11)

Given points are A(1, 5), B(2, 3) and C(- 2, - 11).

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 AC = AB + BC.

Let us find the distances first,

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

⇒ AC = √265 ..... (1)

⇒ AB = √5 ..... (2)

⇒ BC = 2√53 ..... (3)

From (1), (2), (3) we can see that we cannot get any linear relationship.

∴ The three points are not collinear.