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Question

The three vertices of a square ABCD are A(3, 2) B(−2, 2) and D(3, −3). Plot these points on a graph paper and hence, find the coordinates of C. Also, find the area of square ABCD.

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Solution

Let A(3,2), B(-2,2) and D(3,-3) be the three vertices of square ABCD. On plotting the points on the graph paper and joining the points, we see that A, B and D lie in different quadrants. Let C be the fourth vertex of the square. ∴ Abscissa of C = abscissa of B = -2 Also, ordinate of C = ordinate of D = -3 So, coordinates of D = (-2,-3) Let the y-axis cut AB and CD at points L and M, respectively. Now, AB = (BL + LA) = (2 + 3) units = 5 units (Abscissa of B = -2, which indicates that it is on the left side of y-axis. So, for calculating the length of AB, we will consider only the magnitude.) ∴ Area of ABCD = AB × AB = 5 × 5 = 25 sq units

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