We have:
Original
P1(2, -1)
P2(4,1)
P3(5, -1)
P4(4, -4)
New
P1( -1, -2)
P2(1, -4)
P3( -1, -5)
P4( -4, -4)
Then, the transformation is given by:
[tex]\begin{gathered} \text{For P1} \\ (2,-1)\rightarrow(-1,-2)\text{ this is} \\ (x,y)\rightarrow(y,-x) \\ \text{For P2} \\ (4,1)\rightarrow(1,-4) \\ (x,y)\rightarrow(y,-x) \end{gathered}[/tex]Therefore Answer is C.
[tex]f(x,y)=(y,-x)[/tex]