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

Prove that the points (3, 0), (6, 4) and (- 1, 3) are vertices of a right-angled isosceles triangle.

Prove that (2, -2), (-2, 1) and (5, 2) are the vertices of a right angled triangle. Find the area of the triangle and the length of the hypotenuse.

Prove that the points (2, 3), (-4, -6) and (1, 3/2) do not form a triangle.

An equilateral triangle has two vertices at the points (3, 4) and (-2, 3), find the coordinates of the third vertex.