It looks like you've uploaded a photo of a math worksheet with transformations. Let me analyze the problem and help you solve it. Here's what I'll do:

1. Identify the relevant transformations described in the problem.
2. Determine which series of transformations demonstrate congruence.
3. Provide a step-by-step solution and explanation for both Part A and Part B.

Let me start by interpreting the text and providing guidance. I'll transcribe and solve the question.### Problem Analysis

Part A:

The question asks which series of transformations demonstrate that the figures are congruent. The options involve combinations of reflections, translations, and rotations.

Part B:

It describes a sequence of transformations:

1. Figure A is rotated 90° clockwise about the origin.
2. Then, it is translated 2 units up and 1 unit left to form Figure C.

The task is to describe another sequence of transformations to demonstrate congruence between Figures C and B.

Solution to Part A:

To determine the correct series of transformations:

1. Congruence is maintained under rigid motions such as translations, rotations, and reflections.
2. Observing Figures A and B on the coordinate grid:
   • It looks like Figure A could be reflected and/or rotated to align with Figure B.

From the answer options:

• Option B (correct): Reflect Figure A about the y-axis, followed by a 90° clockwise rotation about the origin. This transformation aligns Figure A with Figure B.

Solution to Part B:

To demonstrate congruence between Figures C and B:

1. Transformation of Figure C to Figure B:
   • Looking at the position of Figure C after it was rotated and translated:
     • Reflect Figure C across the y-axis.
     • Rotate 90° clockwise to align with Figure B.

This sequence maintains congruence because reflections and rotations are rigid motions.

Let me know if you’d like a detailed explanation of any specific step or additional clarification! Here are some related questions:

1. What are rigid motions, and why do they preserve congruence?
2. Can multiple sequences of transformations result in the same final figure?
3. How do you determine the center of rotation in transformation problems?
4. Why does a reflection followed by a rotation often change orientation?
5. What are the differences between congruence and similarity in transformations?

Tip: Always verify transformations step by step on a coordinate grid to ensure accuracy.