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.
Let the three vertices of rectangle ABCD be A (2, 2), B (-3, 2) and C (-3, 5)
Now, on plotting these points on the graph paper and by joining the points we get:
The point A lies in the first quadrant while B and C lie in the second quadrant
Let us assume D be the fourth vertex of the rectangle
∴ Abscissa of D = Abscissa of A = 2
And, Ordinate of D = Ordinate of C = 3
Hence, Coordinate of the fourth vertex, D = (2, 5)
Let y-axis cut AB and CD at point L and M respectively
∴ AB = (BL + LA)
= (3 + 2)
= 5 units
Also, BC = 5 – 2
= 3 units
∴ Area of rectangle ABCD = BC × AB
= 3 × 5
= 15 square units
Hence, the area of the rectangle ABCD is 15 square units