Solve this following


Two sides of a parallelogram are along the lines $4 x+5 y=0$ and $7 x+2 y=0 .$ If the equation of one of the diagonals of the parallelogram is $11 x+7 y=9$, then other diagonal passes through the point:


  1. $(1,2)$

  2. (2,2)

  3. (2,1)

  4. (1,3)

Correct Option: , 2


Both the lines pass through origin.

point $D$ is equal of intersection of $4 x+5 y=0 \&$ $11 x+7 y=9$

So, coordinates of point $\mathrm{D}=\left(\frac{5}{3},-\frac{4}{3}\right)$

Also, point B is point of intersection of $7 x+2 y=0$ $\& 11 x+7 y=9$

So, coordinates of point $\mathrm{B}=\left(-\frac{2}{3}, \frac{7}{3}\right)$

diagonals of parallelogram intersect at middle let middle point of $B, D$

$\Rightarrow\left(\frac{\frac{5}{3}-\frac{2}{3}}{2}, \frac{\frac{-4}{3}+\frac{7}{3}}{2}\right)=\left(\frac{1}{2}, \frac{1}{2}\right)$

equation of diagonal $\mathrm{AC}$



diagonal AC passes through $(2,2)$

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