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

Answer 1

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