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in 3D Coordinate Geometry by (50.8k points)
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Show that the points A(1, 1, 1), B(-2, 4, 1), C(1, -5, 5) and D(2, 2, 5) are the vertices of a square.

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Points A(1, 1, 1), B(-2, 4, 1), C(1, -5, 5) and D(2, 2, 5) are the vertices of a square if all sides are of equal measure.

Apply distance formula, and find the distance between all the points:

From above results, AB = BC = CD = AD, and AC = BD

Hence vertices A, B, C, D form a square.

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