[tex]\text{The formula of a distance between two points:}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\text{We have the points}\ (3,\ -4)\ \text{and}\ (3,\ -17).\ \text{Substitute:}\\\\d=\sqrt{(3-3)^2+(-17-(-4))^2}=\sqrt{0^2+(-13)^2}=\sqrt{(-13)^2}=13\\\\Answer:\ \boxed{13\ units}[/tex]
