Q9 of 48 Page 99

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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Prove that the points (1, –2), (3, 0), (1, 2) and (–1, 0) are the vertices of a square.

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Prove that the points (1, 1) (–2, 7) and (3, –3) are collinear.

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