Two consecutive sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0 . If the equation to

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9.Straight Line

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Two consecutive sides of a parallelogram are $4x + 5y = 0$ and $7x + 2y = 0$. If the equation to one diagonal is $11x + 7y = 9$, then the equation to the other diagonal is :-

A

$3x + 7y = 0$

B

$11x -7y = 0$

C

$x -y = 0$

D

$x + y = 0$

Solution

$4 x+5 y=0$ ……$(i)$

$7 x+2 y=0$ ……..$(ii)$

$11 x+7 y=9$ ……..$(iii)$

Solving $(i)$ and $(iii)$

$A \equiv \left( {\frac{5}{3}, – \frac{4}{3}} \right)$

Solving $(ii)$ and $(iii)$

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

Co-ordinates of middle point of $\mathrm{AC}$

$M \equiv \left( {\frac{1}{2},\frac{1}{2}} \right)$

Equation of other diagonal which passes through $\mathrm{O}$ and $\mathrm{M}$ is

$y-0=\frac{\frac{1}{2}-0}{\frac{1}{2}-0}(x-0)$

or $y=x$

Standard 11

Mathematics

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