A reflection over the line y=x is given by:
[tex](x,y)\rightarrow(y,x)[/tex]
Applying this to quadrilateral A'B'C'D' we have:
[tex]\begin{gathered} A^{\prime}(-1,1)\rightarrow A^{\doubleprime}(1,-1) \\ B^{\prime}(-1,2)\rightarrow B^{\doubleprime}(2,-1) \\ C^{\prime}(-2,3)\rightarrow C^{\doubleprime}(3,-2) \\ D^{\prime}(-2,1)\rightarrow D^{\doubleprime}(1,-2) \end{gathered}[/tex]
And the graph of the new quadrilateral A''B''C''D'':
