Question

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 b point c point d point e

Explanation:

Step1: Recall rotation properties

A 180 - degree rotation about a point \(P\) of a figure maps each point \(X\) in the figure to a point \(X'\) such that \(P\) is the mid - point of the line segment \(XX'\).

Step2: Analyze rotation about point \(B\)

If we rotate \(\triangle ABC\) 180° about point \(B\), the image of the triangle will share point \(B\) with the pre - image and will intersect the pre - image at more than one point.

Step3: Analyze rotation about point \(C\)

If we rotate \(\triangle ABC\) 180° about point \(C\), the image of the triangle will share point \(C\) with the pre - image and will intersect the pre - image at more than one point.

Step4: Analyze rotation about point \(D\)

If we rotate \(\triangle ABC\) 180° about point \(D\), the image of the triangle will touch the pre - image only at point \(D\).

Step5: Analyze rotation about point \(E\)

If we rotate \(\triangle ABC\) 180° about point \(E\), the image of the triangle will touch the pre - image only at point \(E\).

Answer:

C. point \(D\)
D. point \(E\)