Question

Prove that the points (2a, 4a), (2a, 6a) and (2a+$\sqrt{3}a$, 5a) are the vertices of an equilateral triangle.

Answer 1

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

In an equilateral triangle all the sides have equal length.

Here the three points are, and.

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

Since all the three sides have equal lengths the triangle has to be an equilateral triangle.