two vertices of an equilateral triangle are (1,1) and (-1,-1) , find the third vertex.

Let ΔABC be the equilateral triangle.

Suppose the coordinates of vertices of ΔABC be A (1, 1), B (– 1, – 1) and C (x, y).

ΔABC is an equilateral triangle.

∴ AB = BC = CA

⇒ AB2 = BC2 = CA2

   (Distance formula)

Thus, the coordinate of third vertex is .

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