Answer :

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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