Prove that the points `(0, 0), (3, (pi)/(2))` and `(3, (pi)/(6))` are the vertices of an equilateral triangle.

Show that the points O(0, 0), A(3, sqrt(3)) "and "B(3, -sqrt(3)) are the vertices of an equilateral triangle. Find the area of this triangle.

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

Show that the points (-3, -3), (3, 3) and (-3sqrt(3), 3sqrt(3)) are the vertices of an equilateral triangle.

Prove that the points (2a, 4a), (2a, 6a) and (2a+ sqrt(3) a, 5a) are the vertices of an equilateral triangle.

Prove that the points A(2, 4), B(2, 6) and C(2 + sqrt(3) , 5) are the vertices of an equilateral triangle.

Prove that the points (0, -1), (6, 7), (-2, 3) and (8, 3) are the vertices of a rectangle.

Prove that the points (4, 8), (0, 2) (3, 0) and (7, 6) are the vertices of a rectangle.

Prove that the points (4, 8), (0, 2), (3, 0) and (7, 6) are the vertices of a rectangle.

Prove that the points (2a,4a),(2a,6a) and (2a+sqrt(3)a,5a) are the vertices of an equilaterall triangle whose side is 2a

If the points (0,0),(2,2sqrt(3)), and (p,q) are the verticesof an equilateral triangle,then (p,q) is