If PS is the median of the triangle with vertices $\mathrm{P}(2,2)$, $\mathrm{Q}(6,-1)$ and $\mathrm{R}(7…
If PS is the median of the triangle with vertices $\mathrm{P}(2,2)$, $\mathrm{Q}(6,-1)$ and $\mathrm{R}(7,3)$, then the equation of the line passing through $(1,-1)$ and parallel to PS is
$4 x+7 y+3=0$
$2 x-9 y-11=0$
$4 x-7 y-11=0$
$2 x+9 y+7=0$
Solution
Since $S$ is the mid point of $Q$ \& $R$
so $\mathrm{S}=\left(\frac{7+6}{2}, \frac{3-1}{2}\right)=\left(\frac{13}{2}, 1\right)$
Now, slope of PS $=m=\frac{2-1}{2-\frac{13}{2}}=\frac{-2}{9}$
Since equation of line passing through $(1,-1)$ and having slope $\frac{-2}{9}$ is
$\begin{aligned}
& y-(-1)=\frac{-2}{9}(x-1) \Rightarrow y+1=\frac{-2 x+2}{9} \\
& \Rightarrow 9 y+9+2 x-2=0 \Rightarrow 2 x+9 y+7=0
\end{aligned}$