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

(5, 1), (1, - 1), (11, 4)

Given points are A(5, 1), B(1, - 1) and C(11, 4).

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 = 3√5 ..... (1)

⇒ AB = 2√5 ..... (2)

⇒ BC = 5√5 ..... (3)

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

∴ The three points are collinear.