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Determine which translations would map Figure KK onto Figure LL.

To determine the translation that maps Figure \( K \) onto Figure \( L \), let's look at the coordinates of a key point on each figure. We can focus on one corner of the shapes to determine how much they need to be moved horizontally and vertically.

1. **Pick a point on Figure \( K \):** Let's choose the bottom-right corner of Figure \( K \). Its coordinates are approximately \( (7, -8) \).
   
2. **Pick the corresponding point on Figure \( L \):** The corresponding corner on Figure \( L \) is at approximately \( (-5, 2) \).

Now, calculate the translation:

- **Horizontal translation (x-direction):** To move from \( x = 7 \) to \( x = -5 \), you need to move left by \( 7 - (-5) = 12 \) units.
- **Vertical translation (y-direction):** To move from \( y = -8 \) to \( y = 2 \), you need to move up by \( 2 - (-8) = 10 \) units.

Thus, the translation that maps Figure \( K \) onto Figure \( L \) is:
- 12 units to the left (negative x-direction).
- 10 units up (positive y-direction).

Do you have any questions or want more details on this? 

Here are some follow-up questions:
1. How can you confirm if the translation you found is correct?
2. What is the general formula for translating a figure in the coordinate plane?
3. Can there be any other transformations, like reflection or rotation, between the two figures?
4. How does translation affect the orientation of the figure?
5. What would happen if the translation were applied in reverse (i.e., moving Figure \( L \) to \( K \))?

**Tip:** When translating shapes on a coordinate plane, always track the movement of both the x and y coordinates carefully to avoid confusion.

Determine which translations would map Figure K onto Figure L.

Learn how to determine the translation that maps Figure K to Figure L using coordinate geometry. This problem involves analyzing the horizontal and vertical shifts needed to align the figures. Suitable for Grades 6-8.

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