Question

Plot A(−3, 0), B(0, 4) and C(3, 4) on graph paper. Plot a point D and write its coordinates if ABCD is a parallelogram. Find its area and perimeter.

Answer 1

Given:

Parallelogram ABCD

A = (−3, 0)

B = (0, 4)

C = (3, 4)

D = (0, 0)

ABCD forms a parallelogram.

Area: 12.0 square units.

Perimeter: 16.0 units

A(–3, 0), B(0, 4), C(3, 4)
To form a parallelogram, D must be (0, 0)

Area = Base × Height

Base = Distance between A(–3, 0) and D(0, 0)

Base = `sqrt((0 + 3)^2 + (0 − 0)^2)`

= `sqrt9`

= 3

vertical height = y-coordinate of B or C = 4

Area = 3 × 4 = 12.0 square units.

Perimeter = 2 × (length of adjacent sides)

Side AB = distance between A(–3, 0) and B(0, 4)

AB = `sqrt((0 + 3)^2 + (4 − 0)^2)`

AB = `sqrt(9 + 16)`

AB = `sqrt25`

AB = 5

Perimeter = 2 × (3 + 5) = 2 × 8 = 16.0 units