Prove that the points `(a, a), (-a, -a) and (-asqrt(3), asqrt(3))` are the vertices of an equilateral triangle.

Explanation

To prove that the points \( (a, a) \), \( (-a, -a) \), and \( (-a\sqrt{3}, a\sqrt{3}) \) are the vertices of an equilateral triangle, we need to show that the distances between each pair of points are equal. We will use the distance formula to calculate the lengths of the sides of the triangle formed by these points.

### Step 1: Define the Points
Let:
- \( A = (a, a) \)
- \( B = (-a, -a) \)
- \( C = (-a\sqrt{3}, a\sqrt{3}) \)

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