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 of the other diagonal is

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Infinity Learn · Accepted Answer

Let the equation of sides AB and AD of the parallelogram ABCD $$be4x+5y=0----(1)$$ and  $$7x+2y=0---(2)respectively$$. Solving (l) and (2), we have x $$=$$ $$0$$, $$y=$$ $$0$$ A $$=$$ (0$$,$$0) Equation of one diagonal of the parallelogram $$is11x+7y=9---(3)Clearly$$, I (0$$, $$0) does not lie on diagonal (3), therefore (3) is the equation of diagonal BD. Solving (1) and (3), we get B≡$$53$$,−$$43$$ and D≡−$$23$$,$$73$$ .  Since H is the middle point of BD∴H≡$$12$$,$$12$$ . Now the equation of diagonal AC which passes through $$A(0$$,$$0)$$ and $$H12$$,$$12$$ is y−$$0=0$$−$$120$$−$$12(x$$−$$0)$$ or  y−$$x=0$$

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 of the other diagonal is

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