Show that the points (3, 4), (–5, 16), (5, 1) are collinear.

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

Let the points be A (3, 4), B (–5, 16) and C (5, 1).

Let

So, in this case if we prove that and are parallel to each other, then we can easily show that A, B and C are collinear.

Therefore, is given by

And is given by

Let us note the relation between and .

We know,

Or …(i)

And we know,

Or

Or …(ii)

Substituting the value of in equation (i), we get

This relation shows that and are parallel to each other.

But also, is the common vector in and .

⇒ and are not parallel but lies on a straight line.

Thus, A, B and C are collinear.