Answer:
The correct option is B.
Step-by-step explanation:
From the given figure it is clear that the A(1,1), B(5,1), C(5,3) and (1,3).
The point of rotation is (3,2).
If a figure rotated 180° about a point (a,b) then
[tex](x,y)\rightarrow (2a-x,2b-y)[/tex]
The figure rotated 180° about the point (3,2) then
[tex](x,y)\rightarrow (2(3)-x,2(2)-y)[/tex]
[tex](x,y)\rightarrow (6-x,4-y)[/tex]
The vertices of image are
[tex]A(1,1)\rightarrow A'(5,3)[/tex]
[tex]B(5,1)\rightarrow B'(1,3)[/tex]
[tex]C(5,3)\rightarrow C'(1,1)[/tex]
[tex]D(1,3)\rightarrow D'(5,1)[/tex]
The vertices of image are same as vertices of preimage. So, after rotation of 180° about the point (3,2) the figure ABCD onto itself.
Therefore the correct option is B.
