Let's go through each question in the image and find the correct answers:

Left Panel (Figures A and B)

1. Are Figure A and Figure B congruent?

   • Answer: Yes, because Figure B appears to be the same shape and size as Figure A; it is just oriented differently on the graph.

2. Which transformation will map Figure A onto Figure B exactly?

   • By observing the graph, it seems that Figure B can be obtained by reflecting Figure A over the $y$-axis.
   • Answer: Reflect Figure A over the $y$-axis.

Right Panel (Figures C and D)

1. Are Figure C and Figure D congruent?

   • Answer: Yes, because Figures C and D have the same shape and size, though they are in different locations.

2. Which transformation will map Figure C onto Figure D exactly?

   • Observing the position of Figure D relative to Figure C, we can see that it’s shifted down by 5 units.
   • Answer: Translate Figure C down 5 units.

Summary of Answers

• Left Panel:

  • Are Figure A and Figure B congruent? Yes
  • Transformation: Reflect Figure A over the $y$-axis

• Right Panel:

  • Are Figure C and Figure D congruent? Yes
  • Transformation: Translate Figure C down 5 units

Would you like further details on these transformations or have any specific questions?

Additional Related Questions

1. What are the properties that define congruent figures?
2. How do reflections affect the coordinates of points on a graph?
3. What is the difference between reflection and rotation transformations?
4. How can translation be represented in terms of coordinate shifts?
5. How does understanding transformations help in geometry problem-solving?

Tip

When determining transformations, try plotting the points of each figure before and after transformation to better understand the effects on position and orientation.