To determine whether a translation maps Figure C onto Figure D, we need to see if there is a consistent shift (translation vector) that moves each point of Figure C to the corresponding point in Figure D.

1. Identify a Corresponding Point in Each Figure: Let's look at the bottom-left corner of Figure C, which is at approximately $(-4, -1)$. The bottom-left corner of Figure D is at approximately $(1, 2)$.

2. Calculate the Translation Vector: To find the translation vector $(x, y)$, we subtract the coordinates of the point in Figure C from the coordinates of the corresponding point in Figure D: $x = 1 - (-4) = 1 + 4 = 5$ $y = 2 - (-1) = 2 + 1 = 3$

   Therefore, the translation vector is $(5, 3)$.

3. Conclusion: A translation of $(5, 3)$ maps Figure C onto Figure D.

Answer:

• The correct option is: "A translation maps Figure C onto Figure D."
• The translation vector is $(5, 3)$.

Would you like further details or have any questions?

Here are some related questions for further exploration:

1. How do you verify if two figures are congruent through transformations?
2. What are the steps to find the translation vector between any two points?
3. How can translations be represented using matrices in linear algebra?
4. What are other types of transformations that can map one figure onto another (like rotations or reflections)?
5. How do translations affect the coordinates of a figure on the coordinate plane?

Tip: When identifying a translation vector, always pick corresponding points that are easy to identify on both figures to minimize calculation errors.