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Prove that the points A(0, 4, 1), B(2, 3...

Prove that the points A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2) are vertices of a square.

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To prove that the points A(0, 4, 1), B(2, 3, -1), C(4, 5, 0), and D(2, 6, 2) are the vertices of a square, we will follow these steps: ### Step 1: Calculate the distances between all pairs of points. We need to find the lengths of the sides (AB, BC, CD, DA) and the diagonals (AC, BD). **Distance Formula in 3D:** The distance \(d\) between two points \(P(x_1, y_1, z_1)\) and \(Q(x_2, y_2, z_2)\) is given by: \[ ...
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