Question

Prove that the points (2,3), (−4, −6) and (1, 3/2) do not form a triangle.

Answer 1

The distance d between two points and is given by the formula

In any triangle the sum of lengths of any two sides need to be greater than the third side.

Here the three points are, and

Let us now find out the lengths of all the three sides of the given triangle.

Here we see that,

This is in violation of the basic property of any triangle to exist. Therefore these points cannot give rise to a triangle.

Hence we have proved that the given three points do not form a triangle.