Answer:
The coordinates of image are R'(1,3) and S'(5,3).
Step-by-step explanation:
From the given figure it is clear that the coordinates of the points R and S are R(-3,-1) and S(-3,-5).
The composition [tex]R_{0,90^{\circ}}\circ r_y[/tex] means the figure reflected across y-axis and then rotate 90 degree counterclockwise about the origin.
If a figure reflected across y-axis then
[tex](x,y)\rightarrow (-x,y)[/tex]
[tex]R(-3,-1)\rightarrow R_1(3,-1)[/tex]
[tex]S(-3,-5)\rightarrow S_1(3,-5)[/tex]
If a figure rotate 90 degree counterclockwise about the origin, then
[tex](x,y)\rightarrow (-y,x)[/tex]
[tex]R_1(3,-1)\rightarrow R'(1,3)[/tex]
[tex]S_1(3,-5)\rightarrow S'(5,3)[/tex]
Therefore the coordinates of image are R'(1,3) and S'(5,3).
