Two adjacent sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0.

If the equation of one of the diagonals is 11x + 7y = 4, find the equation

of the other diagonal.

If the question is "**Two adjacent sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0. If the equation of one of the diagonals is 11x + 7y = 9, find the equation of the other diagonal**", then the solution is given below:

Let AB and AD be consecutive sides of parallelogram ABCD having equations *4x + 5y = 0* and *7x + 2y = 0* respectively. These 2 lines intersect at *A(0, 0)*.

*11x + 7y = 9*

*4x + 5y = 0*

On solving, we get

Thus, coordinates of B are .

Similarly

*11x + 7y = 9 *

*7x + 2y = 0*

On solving, we get the coordinates of D.

Thus, D =

Since diagonals of a parallelogram bisect each other, therefore, P is the mid-point of BD. The coordinates of P are .

Hence, equation of AC is

Cheers!!!

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