Answer:
The correct option is A.
Step-by-step explanation:
The coordinates of rectangle are (5,5), (7,5),(7,9) and (5,9).
If the reflected across the line x=6, it will give the same rectangle because x=6 is line of symmetry.
[tex]900=(720+180)=2(360)+180[/tex]
It means 900 degree clockwise means 180 degree clockwise about (6,7).
Since (6,7) is a center of rectangle. If a rectangle rotated at 180 degree clockwise about center, then it will give the same rectangle.
If a figure rotates 180 degree clockwise about origin, then
[tex](x,y)\rightarrow (-x,-y)[/tex]
If a figure rotates 180 degree clockwise about (a,b), then
[tex](x,y)\rightarrow (2a-x,2b-y)[/tex]
The coordinates after reflection are (5,5), (7,5),(7,9) and (5,9).
The coordinates after rotation are
[tex](5,5)\rightarrow (2(6)-5,2(7)-5)\rightarrow (7,9)[/tex]
[tex](7,5)\rightarrow (2(6)-7,2(7)-5)\rightarrow (5,9)[/tex]
[tex](7,9)\rightarrow (2(6)-7,2(7)-9)\rightarrow (5,5)[/tex]
[tex](5,9)\rightarrow (2(6)-5,2(7)-9)\rightarrow (7,5)[/tex]
The coordinates after reflection followed by rotation are (5,5), (7,5),(7,9) and (5,9).
After the transformation the figure onto itself. Therefore option A is correct.
