a). the the slope of the line through the points 5, 2 and 5, -3
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-3-2}{5-5} \\ m=-\frac{5}{0} \\ m=\infty \end{gathered}[/tex]So the slope is:
[tex]\begin{gathered} \tan \theta=m=\infty \\ \theta=90^{\circ} \end{gathered}[/tex]