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:

  1. 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.



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