The equation of one side of an equilateral triangle is x – y = 0 and one vertex is . Prove that a second side is and find the equation of the third side.

Given: equation of one side of an equilateral triangle is x – y = 0 and one vertex is

To prove: second side is

To find: the equation of the third side.

Explanation:

Let A be the vertex of the equilateral triangle ABC and x − y = 0 be the equation of BC.
Here, we have to find the equations of sides AB and AC, each of which makes an angle of 60∘ with the line x − y = 0

We know the equations of two lines passing through a point x1,y1 and making an angle α with the line whose slope is m.

Here,
x₁, y₁ = 5, α = 60∘, m = 1

So, the equations of the required sides are

and

and

and

and

Hence, the second side is and the equation of the third side is