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



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