Two lines [tex]y_1,y_2[/tex] are perpendicular if their slopes are in a relation [tex]m_1=-\frac{1}{m_2}[/tex].
So we need to find slopes and if the above relation holds then we can claim the lines are perpendicular.
To find slopes, use slope formula
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]
The first slope of a line passing through [tex]PQ[/tex] is
[tex]m_1=\frac{-13-(-9)}{6-2}=\frac{-4}{4}=-1[/tex]
The second slope of a line passing through [tex]RS[/tex] is
[tex]m_2=\frac{-1-(-5)}{5-1}=\frac{4}{4}=1[/tex]
Now check if [tex]m_1=-\frac{1}{m_2}[/tex] is true
[tex]-1=-\frac{1}{1}\implies -1=-1[/tex]
This means the two lines are perpendicular.
Hope this helps.
