Correct answer is option (D).
Given:
Coordinates of point P and S are, P (8,4) and S (8,-1).
The objective is to find the length of the side PS.
Consider the given coordinates as,
[tex]\begin{gathered} (x_1,y_1)=(8,4) \\ (x_2,y_2)=(8,-1) \end{gathered}[/tex]The length between two coordinates can be calculated using the distance formula,
[tex]d=\sqrt[]{(x_2-x_1)^2+(x_2-x_1)^2}[/tex]Substitute the given values in the above formula.
[tex]\begin{gathered} d=\sqrt[]{(8-8)^2+(-1-4)^2} \\ d=\sqrt[]{0^2+(-5)^2} \\ d=\sqrt[]{25} \\ d=\pm5 \end{gathered}[/tex]Since the length cannot be negative, so +5.
Thus, the length of the side PS is, 5 units.
Hence, option (D) is the correct answer.