Given the points :
[tex]\begin{gathered} P=(0,-2) \\ Q=(0,7) \\ R=(3,-5) \\ S=(6,-5) \end{gathered}[/tex]The slope of PQ will be :
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{7-(-2)}{0-0}=\frac{9}{0}[/tex]As the division by zero is undefined, PQ will vertical
The slope od RS will be :
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{-5-(-5)}{6-3}=\frac{-5+5}{3}=\frac{0}{3}=0[/tex]So, the line RS is horizontal
So, the lines PQ and RS are perpendicular
