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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