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
⇒ BC = 5√5 ..... (3)
From (1), (2), (3) we can see that AB + AC = BC.
∴ The three points are collinear.