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

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

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

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 = 5√5 ..... (1)

⇒ AB = 2√5 ..... (2)

⇒ BC = 3√5 ..... (3)

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

∴ The three points are collinear.