https://file.aiquickdraw.com/mathbot/file/1729123506242xblzfkq2.jpg

The problem involves applying the translation rule \((x, y) \to (x + 1, y + 5)\) to each vertex of the triangle on the graph. Let's work through this step by step.

### Coordinates of the original points:
- **A**: Looking at the grid, point \( A \) is at \( (-3, 0) \).
- **B**: Point \( B \) is at \( (-1, -2) \).
- **C**: Point \( C \) is at \( (-4, -3) \).

### Applying the translation \((x, y) \to (x + 1, y + 5)\):
- For **A**: \( (-3 + 1, 0 + 5) = (-2, 5) \)
- For **B**: \( (-1 + 1, -2 + 5) = (0, 3) \)
- For **C**: \( (-4 + 1, -3 + 5) = (-3, 2) \)

### Final coordinates after translation:
- \( A' = (-2, 5) \)
- \( B' = (0, 3) \)
- \( C' = (-3, 2) \)

You can now enter these values into the answer boxes.

Would you like a more detailed explanation of the translation process or help with part b? Here are five related questions:

1. How do translations affect the orientation of geometric shapes?
2. Can translations change the size or shape of a figure?
3. How do we translate a point if the translation rule was \( (x - 2, y + 3) \)?
4. What is the difference between translation and reflection in transformations?
5. How would you translate a figure using vector notation?

**Tip:** Always ensure you're applying the translation rule correctly to both the \(x\)- and \(y\)-coordinates to avoid errors!

Use the graph and the translation (x, y) → (x + 1, y + 5) to answer parts a and b. Enter the image of each vertex as an ordered pair.

Learn how to apply the translation (x, y) → (x + 1, y + 5) on a triangle's vertices in coordinate geometry. This transformation shifts each point horizontally and vertically, demonstrating the impact of translations. Explore the step-by-step solution for each vertex: A (-3, 0), B (-1, -2), C (-4, -3).

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