The base of an equilateral triangle with side 2a lies along the y-axis such that the midpoint of the base is at the origin. Find the vertices of triangle.

A.T.Q., two triangles Δ ABC and Δ A’BC are possible.

Given BC = 2a and mid-point of BC is at 0.

⇒ OB = OC = a

i.e., co-ordinate of B and C are (0,a) and (0,-a), respectively.

As triangles are equilateral, we have on Δ ABC

AB = BC = CA = 2a

Applying Pythagoras theorem

OA =

     =

     = =

     =

Similarly OA’ =

As A and A’ lie on X-axis, coordinates of A and A’ are (, 0) and (-, 0) respectively.

Vertices of

Δ ABC = (0, a), (0, -a), (, 0)

Vertices of

Δ A’BC = (0, a), (0, -a), (-, 0)