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The two consecutive sides of a parallelogram are $\mathrm{4x + 5y = 0}$ and $\mathrm{7x + 2y = 0}$ . If the equation of one of the diagonals is $\mathrm{11x + 7y = 9}$ , find the equation of the other diagonal
Option: 1
$\mathrm{x-y=0}$

Option: 2
$\mathrm{x-2y=0}$

Option: 3
$\mathrm{2x-3y=0}$

Option: 4
$\mathrm{3x-2y=0}$

Answers (1)

best_answer

The sides are $\mathrm{4x+5y=0}\: \: \: \: \: \: \: \: \: \: \: ....(1)$

and $\mathrm{7x+2y=0}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ....(2)$

Equation of the diagonal,

$\mathrm{11x+7y=9}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ....(3)$

Solving (1) and (3) co-ordinates of A are

$\left(\frac{5}{3},-\frac{4}{3}\right)$

Solving (2) and (3) co-ordinates of B are

$\left(-\frac{2}{3}, \frac{7}{3}\right)$

Mid-point of AB is $\mathrm{M\left(\frac{1}{2}, \frac{1}{2}\right)}$

$\therefore$ equation of the diagonal OC is

$\mathrm{y=x \text { or } x-y=0}$

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