Question

The three vertices of a rectangle ABCD are A(2, 2) B(−3, 2) and C(−3, 5). Plot these points on a graph paper and find the coordinates of D. Also, find the area of rectangle ABCD.

Answer 1

Let A(2,2), B(-3,2) and C(-3,5) be the three vertices of rectangle ABCD.
On plotting the points on the graph paper and joining the points, we see that points B and C lie on quadrant II and point A lies on quadrant I.
Let D be the fourth vertex of the rectangle.
So, abscissa of D = abscissa of A = 2
Also, ordinate of D = ordinate of C = 5
So, coordinates of point D = (2,5)
Let the y-axis cut AB and CD at points L and M, respectively.
Now, AB = (BL + LA) = (3 + 2) units = 5 units (Abscissa of B = -3, 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.)
Thus, BC = (5 - 2) units = 3 units
∴ Area of rectangle ABCD = BC × AB = 3 × 5 = 15 sq units