In order to calculate the distance between two points (x1, y1) and (x2, y2), we can use the formula below:
[tex]d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]So, using the points (9, -1) and (9, 8), we have:
[tex]\begin{gathered} d=\sqrt[]{(8-(-1))^2+(9-9)^2} \\ d=\sqrt[]{(8+1)^2+0^2_{}} \\ d=\sqrt[]{9^2+0} \\ d=\sqrt[]{81} \\ d=9 \end{gathered}[/tex]Therefore the distance between the given points is 9 units.