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The base PQ of two equilateral triangles PQR and PQR’ with side 2a lies along y-axis such that the mid-point of PQ is at the origin. Find the coordinates of the vertices R and R’ of the triangles.

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We have two equilateral triangle PQR and PQR' with side 2.a

O is the mid-point of PQ.

In ΔQOR, ΔQOR = 90°

Hence, by Pythagoras theorem

OR2 + OQ2 = QR2

OR2 = (2a)2 - (a)2

OR2 = 3a2

OR = √(3)a

Coordinates of vertex R is (3a,0) and coordinate of vertex R’ is (-3a,0)

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