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.

Explanation

To find the coordinates of the vertices R and R' of the equilateral triangles PQR and PQR', we can follow these steps:

### Step 1: Identify the coordinates of points P and Q
Since the base PQ lies along the y-axis and the midpoint of PQ is at the origin (0, 0), we can determine the coordinates of points P and Q. Given that the length of the base PQ is 2a, the distance from the origin to each point is a. Therefore, the coordinates are:
- Point P: (0, a)
- Point Q: (0, -a)

### Step 2: Determine the coordinates of point R
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