The equation of the base of an equilateral triangle is x + y = 2 and its vertex is (2, -1). Find the length and equations of its sides.

Given: equation of the base of an equilateral triangle is x + y = 2 and its vertex is (2, -1)

To find: length and equations of its sides

Explanation:

Let A (2, − 1) be the vertex of the equilateral triangle ABC and x + y = 2 be the equation of BC.

Diagram:

Here, we have to find the equations of the sides AB and AC, each of which makes an angle of 60∘ with the line x + y = 2

The equations of two lines passing through point x1,y1 and making an angle α with the line whose slope is m is given below:

Here,
x₁ = 2, y₁ = - 1, α = 60∘, m = -1

So, the equations of the required sides are

and

and

Solving x + y = 2 and , we get:

∴ AB = BC = AC =
Hence, equations of its sides are given below: ,