Q. 125.0( 5 Votes )
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
Let A (2, − 1) be the vertex of the equilateral triangle ABC and x + y = 2 be the equation of BC.
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:
x1 = 2, y1 = - 1, α = 60∘, m = -1
So, the equations of the required sides are
Solving x + y = 2 and , we get:
∴ AB = BC = AC =
Hence, equations of its sides are given below: ,
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