Straight Line and Pair of Straight Lines 1 Question 21
21. If $P S$ is the median of the triangle with vertices $P(2,2)$, $Q(6,-1)$ and $R(7,3)$, then equation of the line passing through $(1,-1)$ and parallel to $P S$ is
(2014 Main, 2000)
(a) $4 x-7 y-11=0$
(b) $2 x+9 y+7=0$
(c) $4 x+7 y+3=0$
(d) $2 x-9 y-11=0$
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Solution:
- Coordinate of $S=\frac{7+6}{2}, \frac{3-1}{2}=\frac{13}{2}, 1$
$[\because S$ is mid-point of line $Q R]$
Slope of the line $P S$ is $\frac{-2}{9}$.
Required equation passes through $(1,-1)$ and parallel to $P S$ is
$$ \begin{aligned} y+1 & =\frac{-2}{9}(x-1) \\ \Rightarrow \quad 2 x+9 y+7 & =0 \end{aligned} $$
