To find the graph of the rhombus after the rotation we first need to notice that the vetexes of the original rhombus are:
[tex]\begin{gathered} A(5,1) \\ B(5,6) \\ C(8,10) \\ D(8,5) \end{gathered}[/tex]Now we need to remember that a 180° rotation is given by:
[tex](x,y)\rightarrow(-x,-y)[/tex]Applying it to the vertexes we have:
[tex]\begin{gathered} A(5,1)\rightarrow A^{\prime}(-5,-1) \\ B(5,6)\rightarrow B^{\prime}(-5,-6) \\ C(8,10)\rightarrow C^{\prime}(-8,-10) \\ D(8,5)\rightarrow D^{\prime}(-8,-5) \end{gathered}[/tex]Plotting this new points we have the image of the rhombus after the rotation:
