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

OR^{2} + OQ^{2} = QR^{2}

OR^{2} = (2a)^{2} - (a)^{2}

OR^{2} = 3a^{2}

OR = √(3)a

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