Question

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

• A. reactangle
• B. square
• C. cyclic quadriletral
• D. rhombus

Answer 1

The correct option is D rhombus

$x+3y=4$ .......$\left(1\right)$

Let $m_1$ be the slope of this line

$\Rightarrow m_1=\frac{-1}{3}$

$6x-2y=7$ .......$\left(2\right)$

Let $m_2$ be the slope of this line

$\Rightarrow m_2=\frac{-6}{-2}=3$

Now, $\Rightarrow m_1\times m_2=\frac{-1}{3}\times 3$

$\Rightarrow m_1\times m_2=-1$

Therefore both the lines are perpendicular.

If in a parallelogram, diagonals are perpendicular, then it is a $rhombus$