The base of an equilateral triangle with side 2a lies along the y–axis such that the mid–point of the base is at the origin. Find vertices of the triangle.

Explanation

To find the vertices of an equilateral triangle with a base of length \(2a\) lying along the y-axis, with the midpoint of the base at the origin, we can follow these steps:

### Step 1: Identify the base of the triangle
Since the base of the equilateral triangle lies along the y-axis and the midpoint is at the origin, we can denote the endpoints of the base as points \(B\) and \(C\). Given that the length of the base is \(2a\), the coordinates of points \(B\) and \(C\) can be determined as follows:

- The distance from the origin to each endpoint is \(a\) (half of the base length).
- Therefore, the coordinates of point \(B\) will be \( (0, a) \) and the coordinates of point \(C\) will be \( (0, -a) \).

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