Question

The following figure shows a parallelogram ABCD whose side AB is parallel to the x-axis, $\angle$A = ${60}^{\circ }$ and vertex C = (7, 5). Find the equation of BC and CD.

Answer 1

Since, ABCD is a parallelogram,

B = 180^o - 60^o = 120^o

Slope of BC = tan 120^o = tan (90^o + 30^o) = cot30^o =

Equation of the line BC is given by:

y - y₁ = m(x - x₁)

y - 5 = (x - 7)

y - 5 = x - 7

y = x + 5 - 7

Since, CD || AB and AB || x-axis, slope of CD = Slope of AB = 0

Equation of the line CD is given by:

y - y₁ = m(x - x₁)

y - 5 = 0(x - 7)

y = 5