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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.
Solution
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
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