Question -
Answer -
Given:
The rectangle formedby the lines x = a, x = a’, y = b and y = b’
It is clear that, thevertices of the rectangle are A (a, b), B (a’, b), C (a’, b’) and D (a, b’) .
The diagonal passingthrough 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, thediagonal 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 ofdiagonals are y(a’ – a) – x(b’ – b) = a’b – ab’ and
y(a’ – a) + x(b’ – b)= a’b’ – ab