CBSE Class 10 Maths (Standard) 2015 · Paper 30/2/1 · Question 9

Coordinate Geometry 2 marks Medium

Show that the points

(a, a)

(- a, - a)

and

(- 3 a, 3 a)

are the vertices of an equilateral triangle.

Answer

Since

A B^{2} = B C^{2} = C A^{2} = 8 a^{2}

, the three sides are equal (

A B = B C = C A = 22 ∣ a ∣

), so the points are the vertices of an equilateral triangle.

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