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Prove that the points A (1, 7), B (4, 2), C (−1, −1) and D (−4, 4) are the vertices of a square.

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Let A (1, 7), B (4, 2), C (−1, −1) and D (−4, 4) be the given point. One way of showing that ABCD is a square is to use the property that all its sides should be equal and both its diagonals should also be equal

Now,

Since, AB=BC=CD=DA and , AC=BD all the four sides of the quadrilateral ABCD are equal and its diagonals AC and BD are also equal. Therefore, ABCD is a square

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