# 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’

Concept Used:

The equation of the line passing through the two points ( x1, y1) and ( x2, y2)

To find:

The equation of diagonal of the rectangle.

Explanation:

Clearly, 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

Formula used:  (a’ – a)y – b(a’ – a) = (b’ – b)x – a(b’ – b)

(a’ – a) – (b’ – b)x = ba’ – ab’

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

Formula used:  (a’ – a)y – b(a – a’) = (b’ – b)x – a’(b’ – b)

(a’ – a) – (b’ – b)x = a’b’ – ab

Hence, the equation of diagonals are (a’ – a) – (b’ – b)x = ba’ – ab’ and (a’ – a) – (b’ – b)x = a’b’ – ab

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