The diagonals of a parallelogram ABCD are along the lines $x+3 y=4$ and $6 x-2 y=7$. Then ABCD must be a
The diagonals of a parallelogram ABCD are along the lines $x+3 y=4$ and $6 x-2 y=7$. Then ABCD must be a
rectangle.
square.
rhombus.
cyclic quadrilateral
Solution
Slope of $x+3 y=4$ is $\mathrm{m}_1=-\frac{1}{3}$
Slope of $6 x-2 y=7$ is $m_2=3$
Here, $\mathrm{m}_1 \cdot \mathrm{~m}_2=-1$
$\therefore \quad$ The diagonals are perpendicular to each other.
$\therefore \quad$ Parallelogram ABCD is a rhombus.