# Two diagonals of a parallelogram $ABCD$ are $x+3y=4$ and $6x-2y=7$, then parallelogram represents

If two diagonals of a parallelogram $ABCD$ are along the lines $x+3y=4$ and $6x-2y=7$, then parallelogram represents
(a) rectangle
(b) rhombus
(c) square

$\bf{Attempts}$ with the help of slope

Slope of $x+3y=4$ is $\displaystyle m_{1} = -\frac{1}{3}$ and slope of $6x-2y=7$ is $\displaystyle m_{2} = -\frac{6}{-2} = 3$

So we have $m_{1}\cdot m_{2} = -1$ . So parallelogram represent Rhombus and Square.

But answer given is only Rhombus, could someone explain me the reason, Thanks

• Thanks Parcly Taxel, can we say that option $(c)$ is also true. – DXT Jul 18 '17 at 15:45