Answer:
The correct option is C.
Step-by-step explanation:
From the given figure it is clear that the vertices of the parallelogram are (0,0), (0,-6), (4,-8) and (4,-2).
If a figure rotated 180° about (a,b), then
[tex](x,y)\rightarrow (2a-x,2b-y)[/tex]
If the figure rotated 180° about (2,-4), then
[tex](x,y)\rightarrow (2(2)-x,2(-4)-y)[/tex]
[tex](x,y)\rightarrow (4-x,-8-y)[/tex]
So, the vertices of image after rotated 180° about (2,-4) are
[tex](0,0)\rightarrow (4,-8)[/tex]
[tex](0,-6)\rightarrow (4,-2)[/tex]
[tex](4,-8)\rightarrow (0,0)[/tex]
[tex](4,-2)\rightarrow (0,-6)[/tex]
The vertices of image are same as vertices of preimage. So, 180° rotation about (2,-4) maps the figure onto itself.
Therefore the correct option is C.
