Coordinate Geometry-5

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Show that the triangle formed by the points A(-2, 0), B(2, 0), C(0, 2√3) is equilateral.

Solution: AB2 = (- 2 - 2)2 + (0 - 0)2 = (-4)2 = 16

AC2 = (-2 - 0)2 + (0 - 2√3)2 = (-2)2 + (-2√3)2 = 4 + 12 = 16

BC2 = (2- 0)2 + (0 - 2√3)2 = 4 + 12 = 16

Therefore, AB2 = AC2 = BC2

Therefore, AB = AC = BC

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