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

(0, 0), (9, 6), (3, 2)

Given points are A(0, 0), B(9, 6) and C(3, 2).

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 = √13 ..... (1)

⇒ AB = 3√13 ..... (2)

⇒ BC = 2√13 ..... (3)

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

∴ The three points are collinear.