Question

The diagonals of a parallelogram $PQRS$ are along the lines $x+3y=4$ and $6x-2y=7$, then $PQRS$ must be a

• A. rectangle
• B. square
• C. cyclic quadrilateral
• D. rhombus

Answer 1

Answer: (D)

rhombus

Diagonals of a parallelogram $PQRS$ are along the lines $x+3y=4$ and $6x-2y=7.$

For the line $x+3y=4$. Hence, $m_1=-\frac{1}{3}$.

For the line $6x+-2y=7$. Hence, $m_2=3$

$\therefore m_1\times m_2=-1.$

Therefore, the diagonals of the parallelogram are perpendicular to each

other.

The given parallelogram is a rhombus.