https://file.aiquickdraw.com/mathbot/file/1727199016096u68aivtz.jpg

The problem asks for the image point of \((-1, -7)\) after a translation 4 units to the left and 2 units up.

### Translation steps:
1. **Left by 4 units**: Subtract 4 from the x-coordinate.
   \[
   -1 - 4 = -5
   \]

2. **Up by 2 units**: Add 2 to the y-coordinate.
   \[
   -7 + 2 = -5
   \]

### Image point:
The image point after the translation is \((-5, -5)\).

Would you like further details on how translations work or have any other questions? Here are some follow-up questions for deeper understanding:

1. What are translations in geometry, and how do they affect points?
2. How do translations differ from rotations and reflections?
3. Can translations change the size or shape of a figure?
4. How would the translation change if it was 4 units to the right instead?
5. Can you find the translation rule for different geometric transformations?

**Tip:** In translations, the shape and size of figures do not change—only the position changes.

What is the image point of (-1, -7) after a translation left 4 units and up 2 units?

Find the image point of (-1, -7) after a translation of 4 units to the left and 2 units up. This problem involves key concepts in coordinate geometry, specifically translations. Suitable for middle school students (Grades 6-8).

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