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 .