Answer:
The correct options are 3 and 4.
Step-by-step explanation:
The vertices of the parallelogram are P(-8,6), Q(-2,6), R(0,-3) and S(-6,3).
If a figure reflected about x = -4, then
[tex](x,y)\rightarrow (-x-8,y)[/tex]
Therefore the image is not identical to the original parallelogram.
If a figure reflected about y = 4.5, then
[tex](x,y)\rightarrow (x,-y+9)[/tex]
Therefore the image is not identical to the original parallelogram.
If a figure rotated through an angle of 360° about the origin, then
[tex](x,y)\rightarrow (x,y)[/tex]
Therefore the image is identical to the original parallelogram.
If a figure rotated through an angle of 360° about the vertex R, then
[tex](x,y)\rightarrow (x,y)[/tex]
Therefore the image is identical to the original parallelogram.
Thus the correct options are 3 and 4.
