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} = (a^{2} + b^{2} – 2 ab) + (a^{2} + b^{2} + 2 ab) = 2(a^{2} + b^{2} )

We find that AB = BC = CA.

⇒ Points A, B and C form an equilateral triangle.

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