Let PS be the median of the triangle with vertices $P(2,2)$, $Q(6,-1)$ and $R(7,3)$ The equation of the line passing through $(1,-1)$ and 

Apply formula of slope $\frac{y_2-y_1}{x_2-x_1}$

Equation of line $y-y_1=m(x-x_1)$

$$\begin{gathered} S\text{ is mid point of Q and }R \\ \therefore S=\left(\frac{7+6}{2},\frac{3-1}{2}\right)=\left(\frac{13}{2},1\right) \end{gathered}$$

$\text{ Slope of }\mathrm{PS}=\mathrm{m}=\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}=\frac{2-1}{2-\frac{13}{2}}=\frac{-2}{9}$

$\text{ Equation of the line passing through }(1,-1)\text{ and parllel to }PS\text{ is }\Rightarrow 2\mathrm{x}+9\mathrm{y}+7=0$

$Slope of PR= \frac{1}{5}\Rightarrow slope of line perpendicular ot PR=-5$

$$\begin{gathered} Slope of QR=4 \\ \Rightarrow Slope of perpendicular to QR=\frac{-1}{4} \end{gathered}$$

$Slope of PQ=\frac{-3}{4}$