Question

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

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

Answer 1

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

⇒ AB = 3√13 ..... (2)

⇒ BC = 2√13 ..... (3)

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

∴ The three points are collinear.