Question

If a (-2,1) , b(9,0) , c(4,b) and d (1,a) are vertices of a parallelogram ,abcd . find the values of a and b and hence find the length of each side

Answer 1

In this question we will the concept of straight lines to get a and b.

Parallel lines have the same gradient.

AB is parallel to DC and :

AD is parallel to BC.

Gradient of a line = change in y / change in x

The length of a line = √(y₁ - y₂)² - (x₁ - x₂) ²

From this we get:

a = 8/11

b = 5/11

The lengths of the sides :

AB = DC = 11.045 units

AD = BC = 3.0124 units.

Find working in the image.