Q. 93.9( 8 Votes )

Prove that the points (a, a), (–a, –a) and are the vertices of an equilateral triangle.

Answer :

We have A (a, a)


B (–a, –a)


C ()


Using the distance formula,








We know that (a – b)2 + (a + b)2 = (a2 + b2 – 2 ab) + (a2 + b2 + 2 ab) = 2(a2 + b2 )










We find that AB = BC = CA.


Points A, B and C form an equilateral triangle.


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