Show that the point A (a, a), B (– a, – a) and C(– a√ 3, a√ 3) are the vertices of an equilateral triangle.

For the points A, B and C to be vertices of an equilateral triangle,


AB = BC = CA and we have distance formula,


For two point P(x1, y1) and Q(x2, y2)


PQ= √((x2 – x1)2 + (y2 – y1)2)


Using the above formula, and coordinates we have


AB=√((– a – a)2 + (– a – a)2)


⇒ AB= √(4a2 + 4a2 )=√8 a








As AB = BC = AC


ABC is an equilateral triangle.


19