The task in this image is to identify the translation that maps Figure C to Figure B on the coordinate plane. Here’s how you can determine the translation step-by-step:

1. Choose a reference point: Select a vertex of Figure C (e.g., the bottom left corner of the triangle) and identify its coordinates.
2. Track its destination: Find the corresponding vertex of Figure B and note its coordinates.
3. Calculate the translation: Subtract the coordinates of the vertex in Figure C from the coordinates of the corresponding vertex in Figure B to determine the horizontal and vertical movement.

Let me work this out:

Step 1: Coordinates of a vertex in Figure C

• Choose the vertex at approximately (-8, -5).

Step 2: Coordinates of the corresponding vertex in Figure B

• The corresponding vertex is at approximately (2, -7).

Step 3: Calculate the translation

• Horizontal translation = $2 - (-8) = 10$
• Vertical translation = $-7 - (-5) = -2$

Final Answer:

The translation is 10 units right and 2 units down.

Would you like a more detailed explanation or any additional assistance?

Related Questions:

1. How do translations differ from other transformations like rotations or reflections?
2. What is the mathematical formula for a translation in general?
3. How do you verify if a transformation is a translation?
4. How can you perform a sequence of transformations graphically?
5. What is the impact of negative translations on the coordinates of a figure?

Tip: Always double-check the direction of the translation (positive or negative) when calculating coordinate changes.