Question

Two sides of a parallelogram are along the lines $4x+5y=0$ and $7x+2y=0$. If the equation of one of the diagonals of the parallelogram is $11x+7y=9$, then other diagonal passes through the point

• A. $(2,2)$
• B. $(2,1)$
• C. $(1,3)$
• D. $(1,2)$

Answer 1

The correct option is A $(2,2)$


On solving equation $4x+5y=0$, $7x+2y=0$ and $11x+7y=9$, we get
Coordinate of $D=(-\frac{2}{3},\frac{7}{3})$
Coordinate of $B=(\frac{5}{3},-\frac{4}{3})$
$\therefore$ Mid point of $BD=M=(\frac{1}{2},\frac{1}{2})$
Equation of other diagonal $AC:y=x$
$\therefore$ Point (2, 2) lies on other diagonal