https://file.aiquickdraw.com/mathbot/file/1727453511759g11g0kb8.jpg

The image you provided is about translations in a coordinate plane, where specific points (J', K', L') need to be matched with their pre-image coordinates from the list on the right.

The pre-image point provided is \( (6, -1) \), and the image shows the points on the coordinate plane, which we can label as J', K', and L'. The goal is to identify their pre-image coordinates using translation rules.

Let’s solve this step by step:

1. Identify the coordinates of J', K', and L' from the graph.
2. Match each of these coordinates with the given options on the right.
   
### Coordinates from the graph:
- J' ≈ \( (0, 0) \)
- K' ≈ \( (-1, -1) \)
- L' ≈ \( (-2, -3) \)

Now, we’ll compare these image points with the pre-image coordinates listed on the right:
- \( (6, -3) \)
- \( (6, -5) \)
- \( (-4, -6) \)
- \( (3, -10) \)
- \( (-4, -4) \)
- \( (-3, -8) \)
- \( (3, -8) \)
- \( (6, -10) \)

Each translation would follow a consistent rule (e.g., moving right by a fixed number and down by another). You can use this information to match each pre-image to the appropriate translation based on how the points are positioned on the graph.

Would you like more details on how translations work, or further clarifications? Also, here are five questions related to translations to help you practice:

1. How would you describe a translation in terms of shifts along the x-axis and y-axis?
2. What is the relationship between pre-image and image points in translation?
3. How can you verify if two points are related by a translation?
4. What is the rule of translation when moving a point \( n \) units right and \( m \) units down?
5. How do translations differ from other types of transformations like reflections or rotations?

**Tip:** When matching coordinates, always observe the shift pattern between the original and translated points.

Drag the image coordinates at the right to match the correct pre-image coordinate.

Learn how to perform translations in the coordinate plane and match image coordinates to their pre-image points. This problem involves understanding translations and coordinate geometry, ideal for Grades 6-8.

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