Let's begin by listing out the information given to us:
[tex]\begin{gathered} P\mleft(-3,5\mright)=(x_1,y_1) \\ S\mleft(6,9\mright)=(x_2,y_2) \end{gathered}[/tex]
The formula for distance between two points is given by:
[tex]d=\sqrt{\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
The next step is to substitute the values into the formula:
[tex]\begin{gathered} d=\sqrt[]{\mleft({-3_{}-6}\mright)^2+\mleft({5-9}\mright)^2} \\ d=\sqrt[]{(-9)^2+(-4)^2}=\sqrt[]{81+16}=\sqrt[]{97} \\ d=\sqrt[]{97}units \end{gathered}[/tex]
Hence, option d is the correct answer
