Q. 2

# 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)

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