We have the general rule for a rotation of 90° counterclockwise:
[tex]r_{90}(x,y)=(y,-x)[/tex]
and the general rule for a y=-x reflection is:
[tex]r_{y=-x}(x,y)=(-y,-x)[/tex]
In this case, we have the points R=(2,-2), S=(5,-1) and T=(3,-5).
Then, we first have to use the 90° rotation on all points:
[tex]\begin{gathered} r_{90}(R)=r_{90}(2,-2)=(-2,-2)=R^{\prime} \\ r_{90}(S)=r_{90}(5,-1)=(-1,-5)=S^{\prime} \\ r_{90}(T)=r_{90}(3,-5)=(-5,-3)=T^{\prime} \end{gathered}[/tex]
Now we use the y=-x reflection on our new points:
[tex]\begin{gathered} r_{y=-x}(R^{\prime})=r_{y=-x}(-2,-2)=(2,2)=R^{\doubleprime} \\ r_{y=-x}(S^{\prime})=r_{y=-x}(-1,-5)=(5,1)=S^{\doubleprime} \\ r_{y=-x}(T^{\prime})=r_{y=-x}(-5,-3)=(3,5)=T^{\doubleprime} \end{gathered}[/tex]
therefore, the final points after the transformations are:
R''=(2,2)
S''=(5,1)
T''=(3,5)
