The slope of QR is,
[tex]\begin{gathered} m_{QR}=\frac{10-2}{9-(-5)} \\ =\frac{8}{14} \\ =\frac{4}{7} \end{gathered}[/tex]
The slope of ST is,
[tex]\begin{gathered} m_{ST}=\frac{-8-(-1)}{-2-2} \\ =\frac{-7}{4} \end{gathered}[/tex]
Thus,
[tex]\begin{gathered} m_{QR}\times m_{ST}=\frac{4}{7}\times\frac{-7}{4} \\ =-1 \end{gathered}[/tex]
As the product of slope is -1 QR and ST are perpendicular.
