Find the equations to the diagonals of the rectangle the equations of whose sides are x = a, x = a’, y = b and y = b’.

Given:

The rectangle formed by the lines x = a, x = a’, y = b and y = b’

It is clear that, the vertices of the rectangle are A (a, b), B (a’, b), C (a’, b’) and D (a, b’) .

The diagonal passing through A (a, b) and C (a’, b’) is

By using the formula,

(a’ – a)y – b(a’ – a) = (b’ – b)x – a(b’ – b)

(a’ – a) – (b’ – b)x = ba’ – ab’

Similarly, the diagonal passing through B (a’, b) and D (a, b’) is

By using the formula,

(a’ – a)y – b(a – a’) = (b’ – b)x – a’ (b’ – b)

(a’ – a) + (b’ – b)x = a’b’ – ab

The equation of diagonals are y(a’ – a) – x(b’ – b) = a’b – ab’ and

y(a’ – a) + x(b’ – b) = a’b’ – ab