The three vertices of a rectangle ABCD are A(3, 2), B(–2, 2) and C(3, –3). Plot these points on a graph paper and find the coordinates of D. Also, find the area of rectangle ABCD.
Let the three vertices of rectangle ABCD be A (3, 2), B (-2, 2) and D (3, -3)
Now, on plotting these points on the graph paper and by joining the points we get:
A, B and D lie in different quadrants
Let us assume D be the fourth vertex of the rectangle
∴ Abscissa of C = Abscissa of B = - 2
And, Ordinate of C = Ordinate of D = - 3
Hence, Coordinate of the fourth vertex, C = (-2, -3)
Let y-axis cut AB and CD at point L and M respectively
∴ AB = (BL + LA)
= (2 + 3)
= 5 units
∴ Area of rectangle ABCD = AB × AB
= 5 × 5
= 25 square units
Hence, the area of the rectangle ABCD is 25 square units