Q. 74.1( 7 Votes )

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

Answer :


Let ABC be the given equilateral triangle with side 2a


AB= BC = AC = 2a


Assuming that the base AB lies on the y axis such that the mid-point of AB is at the origin


i.e.BO = OA = a and O is the origin


⇒ Co-ordinates of point A are (0,a) and that of B are (0,-a)


Since the line joining a vertex of an equilateral ∆ with the mid-point of its opposite side is perpendicular


Vertex of A lies on the y –axis


On applying Pythagoras theorem


(AC)2 = OA2 + OC2


(2a)2= OA2 + a2


4a2 – a2 = OA2


3a2= OA2


OA =


Co-ordinates of point C =


Thus, the vertices of the given equilateral triangle are (0, a) , (0, -a) , (


Or (0, a), (0, -a) and (

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