Question

The following figure shows a parallelogram ABCD whose side AB is parallel to the x-axis, ∠A = 60° and vertex C = (7, 5). Find the equations of BC and CD.

Answer 1

Since, ABCD is a parallelogram,

∠A + ∠B = 180°

∠B = 180° – 60° = 120°

Slope of BC = tan 120° = tan (90° + 30°) = cot 30° = `sqrt(3)`

Equation of the line BC is given by:

y − y₁ = m(x − x₁)

`y - 5 = sqrt(3)(x - 7)`

`y - 5 = sqrt(3)x - 7sqrt(3)`

`y = sqrt(3)x + 5 - 7sqrt(3)`

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