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Distance Formula

Points 1,1,1,...

Question

Points (1, 1, 1), (–2, 4, 1), (–1, 5, 5) and (2, 2, 5) are the vertices of a

A

Rectangle

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B

Square

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C

Parallelogram

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D

Trapezium

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Solution

The correct option is B
Square

Let A = (1, 1, 1); B=(-2, 4, 1); C=(-1, 5, 5)& D =(2, 2, 5) AB = $\sqrt{9 + 9 + 0} = 3 \sqrt{2}, B C = \sqrt{1 + 1 + 16} = 3 \sqrt{2} a n d C D = 3 \sqrt{2} a n d A D = 3 \sqrt{2} .$
Hence it is a square.

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