90-degree clockwise rotation transforms the coordinates the following way:
[tex](x,y)\rightarrow(y,-x)[/tex]Now, after performing 90-degree clockwise rotation, we also move our point 3 units down, meaning, the final coordinates of the point are
[tex](y,-x-3)[/tex]Now we are told that the coordinates of the resultant point are
[tex](1,-4)[/tex]meaning
[tex]\begin{gathered} y=1 \\ -x-3=-4 \\ \end{gathered}[/tex]Solving for x gives
[tex]\begin{gathered} y=1 \\ x=1 \end{gathered}[/tex]Hence, the coordinates of the original point are
[tex](1,1)[/tex]which is choice D.
