Straight Line and Pair of Straight Lines 1 Question 33
33. The diagonals of a parallelogram $P Q R S$ are along the lines $x+3 y=4$ and $6 x-2 y=7$. Then, $P Q R S$ must be a
(a) rectangle
(b) square
(c) cyclic quadrilateral
(d) rhombus
$(1998,2 M)$
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Solution:
- Slope of line $x+3 y=4$ is $-1 / 3$ and slope of line $6 x-2 y=7$ is 3 .
Here, $\quad 3 \times \frac{-1}{3}=-1$
Therefore, these two lines are perpendicular which show that both diagonals are perpendicular.
Hence, $P Q R S$ must be a rhombus.
