Geometry (C10)

The points A(4, –2), B(7, 2), C(0, 9) and D(–3, 5) form a parallelogram. Find the length of the altitude of the parallelogram on the base AB.

Answer

Let the height of parallelogram taking AB as base be h.

Now, AB = √[(7-4)2 + (2+2)2]

AB = √(32 + 42) = 5 units

Area (Δ ABC) = ½[4(2 - 9) + 7(9 + 2) + 0(-2 - 2)]

Area (Δ ABC) = 49/2 sq units

Now, ½ × AB × h = 49/2

½ × 5 × h = 49/2

h = 49/5

h = 9.8 units