If the co-ordinates of the vertices of an equilateral triangle with sides of length ‘a’ are (x 1 , y 1 ), (x 2 , y 2 ), (x 3 , y 3 ), then

Question

Philoid · Accepted Answer

The coordinates of the vertices of an equilateral triangle are (x₁, y₁), (x₂, y₂), (x₃, y₃).

So, the area of triangle with given vertices is given by

Given that the length of the sides of an equilateral triangle = a

Also, area of equilateral triangle =

Now, squaring both the sides, we get

Hence Proved