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

${\displaystyle \frac{y-11}{12-11}=\frac{x-8}{10-8}}$

∴ ${\displaystyle \frac{y-11}{1}=\frac{x-8}{2}}$

∴ 2y – 22 = x – 8

∴ x – 2y + 14 = 0

Equation of diagonal BD is ${\displaystyle \frac{y-11}{12-11}=\frac{x-10}{8-10}}$

∴ ${\displaystyle \frac{y-11}{1}=\frac{x-10}{-2}}$

∴ –2y + 22 = x – 10

∴ x + 2y = 32