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  • Two sides of a parallelogram are along the lines . If the equation of one of the diagonals of the parallelogram is <img alt="11 x+7

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
Option: 1 \left ( 1,2 \right )
Option: 2 \left ( 2,2 \right )
Option: 3 \left ( 2,1 \right )
Option: 4 \left ( 1,3 \right )

Answers (1)

best_answer

Clearly point of intersection A$ is $(0,0)
D \text { is }\left(\frac{5}{3},-\frac{4}{3}\right) \text { \& } B \text { is }\left(-\frac{2}{3}, \frac{7}{3}\right)

As diagonals bisect each other, so other diagonal passes through mid point of B D (i.e.E)

E is \left(\frac{1}{2}, \frac{1}{2}\right)

Equation \: \: of BC\: \: is

\begin{aligned} &y-0=\left(\frac{\frac{1}{2}-0}{\frac{1}{2}-0}\right)(x-0) \\ &\Rightarrow y=x . \end{aligned}

It passes through (2,2)

The option (2) is correct.

Posted by

Kuldeep Maurya

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