The midpoint formula for a segment is:
[tex]x_m,y_{_m}=\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2}[/tex]apply to points R and P
[tex]\begin{gathered} x_m,y_m=\frac{(5+3)}{2},\frac{(8+6)}{2} \\ x_m,y_m=\frac{8}{2},\frac{14}{2} \\ x_m,y_m=(4,7) \end{gathered}[/tex]using the definition of slope find the slope of the segment
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]apply to points R and P
[tex]\begin{gathered} m=\frac{8-6}{5-3} \\ m=\frac{2}{2} \\ m=1 \end{gathered}[/tex]to lines are parallel when the slopes are the same
[tex]\mleft\Vert m=1\mright?[/tex]two lines are perpendicular when the product of the slopes is equal to -1
[tex]\begin{gathered} m\cdot\perp m=-1 \\ 1\cdot\perp m=-1 \\ \perp m=-\frac{1}{1} \\ \perp m=-1 \end{gathered}[/tex]