Question

On a coordinate plane, parallelogram A B C D is shown. Point A is at (1, 3), point B is at (8, 8), point C is at (12, 5), and point D is at (5, 0).
If line segment AB measures approximately 8.6 units and is considered the base of parallelogram ABCD, what is the approximate corresponding height of the parallelogram? Round to the nearest tenth.

3.7 units
4.1 units
4.8 units
5.6 units

Answer 1

Area = |det(AB, AD)| where AB = (7, 5) and AD = (4, −3).
det = 7(−3) − 5(4) = −21 − 20 = −41, so area = 41.

Height = area / |AB| = 41 / sqrt(7^2+5^2) = 41 / sqrt(74) ≈ 41 / 8.602 ≈ 4.8.

Answer: 4.8 units.