if two lines are perpendicular to each other, the product of their slope is -1.
so,... .hmmm let's check the slope of each one, and their product then.
[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -5}}\quad ,&{{ 10}})\quad
% (c,d)
&({{ -9}}\quad ,&{{ 2}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{2-10}{-9-(-5)}\implies \cfrac{2-10}{-9+5}
\\\\\\
\cfrac{-8}{-4}\implies \stackrel{\textit{slope for PQ}}{2}\\\\
-------------------------------[/tex]
[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 4}}\quad ,&{{ 6}})\quad
% (c,d)
&({{ -4}}\quad ,&{{ 10}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{10-6}{-4-4}\implies \cfrac{4}{-8}
\\\\\\
\stackrel{\textit{slope for RS}}{-\cfrac{1}{2}}\\\\
-------------------------------\\\\
\stackrel{mPQ}{2}\cdot \stackrel{mRS}{-\cfrac{1}{2}}\implies -\cfrac{2}{2}\implies -1[/tex]
