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 a rectangle ABCD.
Let the y-axis cut the rectangle ABCD at the points L and M respectively.

Abscissa of D = Abscissa = A = 2
Ordinate of D = Ordinate of C = 5
`:.` coordinates of D are (2, 5)
`AB = (BL + LA) = (3 + 2)` units = 5 units.
`BC = (5-2)` units = 3 units.
ar(rectangle ABCD) `= (AB xx BC)`
`= (5 xx 3)`sq units
= 15 sq units.