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
