Straight Line and Pair of Straight Lines 1 Question 32
32. If $P(1,2), Q(4,6), R(5,7)$ and $S(a, b)$ are the vertices of a parallelogram $P Q R S$, then
$(1998,2 M)$
(a) $a=2, b=4$
(b) $a=3, b=4$
(c) $a=2, b=3$
(d) $a=3, b=5$
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Solution:
- $P Q R S$ is a parallelogram if and only if the mid point of the diagonals $P R$ is same as that of the mid-point of $Q S$. That is, if and only if
$$ \begin{array}{rlrl} & \frac{1+5}{2} & =\frac{4+a}{2} \text { and } \frac{2+7}{2}=\frac{6+b}{2} \\ \Rightarrow \quad a & =2 \text { and } b=3 . \end{array} $$
