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.

Question

Philoid · Accepted Answer

Since PQ is the base of two equilateral triangles with side 2a and mid-point of PQ is at origin.

Therefore point R lies on positive x-axis and point R’ lies on negative y-axis.

OR² = (2a)²- a²

OR² = 4a²- a²

OR = √3a

Therefore coordinates of R are ( √3a, 0) and R’ (0, √3a)