If the points A (m, –1), B (2, 1) and C(4, 5) are collinear, find the value of m.

Let us understand that, two more points are said to be collinear if they all lie on a single straight line.

We have been given points:

A (m, –1), B (2, 1) and C (4, 5).

These points are collinear.

Let us define the position vectors as,

Now, we need to find the vectors and .

is given by

And is given by

Since, A, B, C and D are collinear. We can draw a relation between and .

Putting the values of and , we get

Comparing L.H.S and R.H.S, we get

2 – m = 2λ

And 2 = 4λ

We need to find the value of λ in order to find m.

We have

2 = 4λ

Putting the value of λ in equation (2 – m) = 2λ

⇒ 2 – m = 1

⇒ m = 2 – 1

⇒ m = 1

Thus, the value of m = 1.