Question

Susan will rotate triangle ABC 180° about one of the labeled points. Susan says, "The image will not touch the pre-image at all."

Which points could be her center of rotation?

Select each correct answer.

point C

point D

point E

point F

Answer 1

Point E and F I think

Answer 2

The correct options are 3 and 4.

Explanation:

It is given that Susan will rotate triangle ABC 180° about one of the labeled points.

We need to find the center of rotation, so that the image will not touch the pre-image at all.

The given points are A, B, C, D, E, F.

Points A, B and C vertices of the triangle. If triangle rotated 180° about its vertices then image and preimage are connected at that vertices.

Point D lies inside the triangle. If triangle rotated 180° about point D then image and preimage will touch each other.

Points E and F lie outside the triangle. If triangle rotated 180° about point E or F then image and preimage of triangle are on the opposite sides of the point or rotation.

So we can conclude that the image will not touch the pre-image at all if it is rotated 180° about point E or F.

Therefore the correct options are 3 and 4.