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To map Figure \( K \) onto Figure \( L \) through a translation, we need to determine how many units to move Figure \( K \) horizontally (along the \( x \)-axis) and vertically (along the \( y \)-axis) to align it perfectly with Figure \( L \).

Let's analyze the coordinates of corresponding points in Figures \( K \) and \( L \):

1. **Point at bottom left of Figure K**: The coordinates are approximately \((5, -7)\).
2. **Point at bottom left of Figure L**: The coordinates are approximately \((-4, 2)\).

Now, we calculate the horizontal and vertical translations needed:

- **Horizontal translation (along the \( x \)-axis)**: To go from \( x = 5 \) to \( x = -4 \), the translation is \( -4 - 5 = -9 \) units.
- **Vertical translation (along the \( y \)-axis)**: To go from \( y = -7 \) to \( y = 2 \), the translation is \( 2 - (-7) = 9 \) units.

Thus, the translation that maps Figure \( K \) onto Figure \( L \) is \( 9 \) units **up** and \( 9 \) units **left**.

Would you like a more detailed explanation or further questions about this?

Here are five related questions for deeper exploration:
1. What is the rule for translations in the coordinate plane?
2. How can we verify if the entire figure translates correctly, not just one point?
3. What other transformations (like reflections or rotations) could map Figure \( K \) to \( L \)?
4. How does translation affect the orientation and size of a figure?
5. Can you think of a real-world application where translations are useful?

**Tip**: When translating a shape, always check the corresponding vertices to ensure the entire figure is moved consistently.

Determine which translations would map Figure K onto Figure L.

Learn how to map Figure K onto Figure L by determining the horizontal and vertical translation units. This geometry problem involves moving shapes on a coordinate plane and covers key concepts like translation formulas and theorems. Suitable for students in Grades 6-8.

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