Latrell will rotate △abc 180° about one of the labeled points. latrell says, “the image will only touch the pre-image at exactly one point.” which points could be his center of rotation? select each correct answer. point a point b point c point d point e point f

The question is asking to choose among the following choices that states the point that could be the center of the rotation and in my further understanding and analysis, I would say that it would be the new point in the center. I hope you are satisfied with my answer and feel free to ask for more 

X²-12x=64x²-12x+36=64+36(x-6)(x-6) = 100(x-6)² = 100x-6 = 10x=16