Question

Help please

Tasha sketched the image of trapezoid EFGH after a 180° rotation about the origin. Then, she sketched a second image of EFGH after a 540° rotation about the origin. How are the two rotations of EFGH related? Explain.

A. The two rotations map the same image onto EFGH since 180° is a full rotation and 180° + 180° + 180° = 150°.

B. The two rotations are not related since 360° is a full rotation. Any rotations less than 360° maps the pre-image onto itself.

C. The rotations are not related since 360° is a full rotation. Any rotation greater 360° maps the pre-image onto itself.

D. The two rotations map the same image since 350° is a full rotation and 180° + 360° = 540°

Answer 1

Option A is incorrect because 180° rotation is not a full rotation. It maps the image onto its reflection across the origin.

Option B is incorrect because rotations greater than 360° can also map the image onto itself.

Option C is partially correct, but it is not a complete explanation. Rotations greater than 360° can map the pre-image onto itself, but not all rotations greater than 360° do so.

Option D is incorrect because 350° is not a full rotation, and 180° + 360° = 540° is not a relevant calculation.

The correct answer is: The two rotations are related because 540° is equivalent to 1.5 full rotations, which means that the second rotation maps the image onto its original position. In other words, the second rotation undoes the first rotation, so the two rotations combined result in a net rotation of 360°, which maps the image onto itself.

Answer 2

Answer: D. The two rotations map the same image since 350° is a full rotation and 180° + 360° = 540°.