Let’s analyze the question in your image step by step.

Given:

We are tasked with determining how Figure A can be transformed into Figure B, and whether the two figures are similar.

Part (a): Transformation Steps

Looking at Figure A and Figure B:

1. Figure B is larger than Figure A, indicating that a dilation (scaling) is required.
2. Figure B is inverted horizontally, suggesting a reflection over the y-axis is involved.
3. Figure B’s position is different from Figure A’s original position, so some kind of translation or rotation may also be required.

Now we analyze the options:

• Option 1: Translate Figure A to the right 5 units, then dilate with scale factor 2 at the origin.

  • Translation does not account for the inversion.
  • This option is incorrect.

• Option 2: Reflect Figure A over the y-axis, then dilate with scale factor 2 at the origin.

  • Reflecting over the y-axis flips the figure horizontally.
  • Dilating it by scale factor 2 enlarges it appropriately.
  • This matches the transformation required to map Figure A to Figure B. (Correct)

• Option 3: Dilate Figure A with scale factor 2 at the origin, then reflect over the y-axis.

  • Dilating first and then reflecting also achieves the correct result.
  • This is another valid sequence. (Correct)

• Option 4: Dilate Figure A with scale factor 2 at the origin, then rotate clockwise $90^\circ$.

  • Rotation is not necessary as Figure B is not rotated relative to Figure A.
  • This option is incorrect.

• Option 5: None of these.

  • Since options 2 and 3 work, this is incorrect.

Answer for (a): Options 2 and 3.

Part (b): Are Figure A and Figure B Similar?

Two figures are similar if one can be obtained from the other through a sequence of rigid transformations (translations, reflections, rotations) and/or dilations.

• Since Figure B can be obtained from Figure A through a reflection and a dilation, the figures are similar.

Answer for (b): Yes.

Final Answers:

1. (a) Options 2 and 3.
2. (b) Yes, they are similar.

Do you want more detailed explanations for these transformations or the similarity concept?
Here are five related questions to deepen your understanding:

1. What is the difference between a reflection and a rotation in transformations?
2. How can you determine the scale factor of a dilation?
3. What are the key criteria for two figures to be similar?
4. How does a dilation affect the orientation of a figure?
5. Can two figures be congruent but not similar? Why or why not?

Tip: Always check the sequence of transformations step by step and test whether each change matches the final figure's properties!