Question

The points A(6,1), B(8,2), C(9,4) and D(7,3) ate the vertices of a parallelogram. Find the lenght and te altitude of the parallelogram on the base AB.

Answer 1

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

Now, AB = √[(8-6)² + (2-1)²]

Length of base AB = √(2² + 1²) = √5 units

Area (Δ ABC) = ½ (x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) = ½[6(2 - 4) + 8(4 - 1) + 9(1 - 2)]

Area (Δ ABC) = ½[[ -12 + 24 -9] = 3/2 sq units

Now, ½ × AB × h = 3/2

½ ×√5 × h = 3/2

h = 3/√5

So altitude, h = 1.34 units