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

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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