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.