Two adjacent sides of a parallelogram are 4x | vedclass

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(C) Since the given lines intersect at the origin $O$,one vertex of the parallelogram is $O(0, 0)$.Let the vertices $A$ and $B$ be the intersection po

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$x - y = 0$

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(C) Since the given lines intersect at the origin $O$,one vertex of the parallelogram is $O(0, 0)$.Let the vertices $A$ and $B$ be the intersection points of the sides $4x + 5y = 0$ and $7x + 2y = 0$ with the diagonal $11x + 7y - 9 = 0$ respectively.Solving the systems of equations,we find the coordinates of $A$ and $B$ as $A = (5/3, -4/3)$ and $B = (-2/3, 7/3)$.The midpoint $M$ of the diagonal $AB$ is given by $(\frac{5/3 - 2/3}{2}, \frac{-4/3 + 7/3}{2}) = (1/2, 1/2)$.The other diagonal passes through the origin $O(0, 0)$ and the midpoint $M(1/2, 1/2)$.The equation of the line passing through $(0, 0)$ and $(1/2, 1/2)$ is $y = x$,or $x - y = 0$.

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

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