Problem says that Latrell will rotate △ABC 180° about one of the labeled points B, C, D or E. Latrell says, “The image will only touch the pre-image at exactly one point.”. Now we need to select the correct choice from the given four choices.
We know that if center of rotation lies inside the rotating picture then there will be lot's of common points in pre-image and the new image. So point E will not work.
point D lies on side AB so few points that lie on side AB will be common in pre-image and the new image. So point D will also not work.
Rotating about any corner point will not produce any common point in the pre-image and the new image. B and C are the corner points.
So point B and point C are the final answer.
