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.

Answer 1

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