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)