Two adjacent sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0 If - Maths - Straight Lines

Question

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

ramandeep.singh · Accepted Answer

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 $x = \frac{5}{3} y = \frac{- 4}{3}$ Thus, coordinates of B are $(\frac{5}{3}, \frac{- 4}{3})$ Similarly 11x + 7y = 9 7x + 2y = 0 On solving, we get the coordinates of D Thus, D = $(\frac{- 2}{3}, \frac{7}{3})$ Since diagonals of a parallelogram bisect each other, therefore, P is the mid-point of BD The coordinates of P are $(\frac{1}{2}, \frac{1}{2})$ Hence, equation of AC is $y - 0 = \frac{\frac{1}{2} - 0}{\frac{1}{2} - 0} (x - 0) \Rightarrow y = x$ Cheers!!!

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 equationof the other diagonal.

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.