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Question
Answer the following question:
Find the equations of the diagonals of the rectangle whose sides are contained in the lines x = 8, x = 10, y = 11 and y = 12
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Solution
Given, equations of sides of rectangle are x = 8, x = 10, y = 11 and y = 12
From the above diagram,
Vertices of rectangle are A(8, 11), B(10, 11), C(10, 12) and D(8, 12).
Equation of diagonal AC is
`(y - 11)/(12 - 11) = (x - 8)/(10 - 8)`
∴ `(y - 11)/1 = (x - 8)/2`
∴ 2y – 22 = x – 8
∴ x – 2y + 14 = 0
Equation of diagonal BD is `(y - 11)/(12 - 11) = (x - 10)/(8 - 10)`
∴ `(y - 11)/1 = (x - 10)/(-2)`
∴ –2y + 22 = x – 10
∴ x + 2y = 32
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