Q. Two consecutive sides of a parallelogram are $4x + 5y = 0$ and $7x + 2y = 0$. One diagonal of the parallelogram is $11x + 7y = 9$. If the other diagonal is $ax + by + c = 0$, then
A) $a = - 1,\ b = - 1,\ c = 2$
B) $a = 1,\ b = - 1,\ c = 0$
C) $a = - 1,\ b = - 1,\ c = 0$
D) $a = 1,\ b = 1,\ c = 1$
Explanation
(b)
Since, the coordinates of three verities $A,\ B$ and $C$ are $\left( \frac{5}{3},\ - \frac{4}{3} \right),\ (0,\ 0)$ and $\left( - \frac{2}{3},\frac{7}{3} \right)$ respectively. Also, the mid point of $AC$ is $\left( \frac{1}{2},\frac{1}{2} \right)$ Therefore, the equation of line passing through $\left( \frac{1}{2},\frac{1}{2} \right)$ and $(0,\ 0)$ is $x - y = 0$, which is the required equation of another diagonal
$\therefore\ a = 1,\ b = - 1$ and $c = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.