https://file.aiquickdraw.com/mathbot/file/1731124758399yu88sqkr.jpg

To apply the translation \((x, y) \rightarrow (x + 4, y - 3)\) to each point of \(\triangle ABC\), let's calculate the new coordinates:

1. **Point \(A(-5, 2)\):**
   \[
   A' = (-5 + 4, 2 - 3) = (-1, -1)
   \]

2. **Point \(B(-3, 4)\):**
   \[
   B' = (-3 + 4, 4 - 3) = (1, 1)
   \]

3. **Point \(C(-2, 0)\):**
   \[
   C' = (-2 + 4, 0 - 3) = (2, -3)
   \]

The coordinates of the new triangle \(\triangle A'B'C'\) are:
- \(A' = (-1, -1)\)
- \(B' = (1, 1)\)
- \(C' = (2, -3)\)

Would you like to delve deeper into translation transformations or have any questions?

Here are five related questions to explore further:
1. How does translating a figure affect its orientation and size?
2. What are some real-world applications of geometric translations?
3. How would the triangle’s position change with different translation vectors?
4. Can you describe the transformation if we reversed the translation direction?
5. What other transformations besides translation could be applied to \(\triangle ABC\)?

**Tip:** Visualizing transformations on a graph helps solidify understanding of coordinate changes.

Translate \( \triangle ABC \) according to the translation rule \( (x, y) \rightarrow (x + 4, y - 3) \). List the coordinates of the new triangle \( \triangle A'B'C' \).

Learn how to translate triangle ABC by applying the translation rule (x, y) → (x + 4, y - 3). This problem involves calculating new coordinates for points A, B, and C and covers key concepts in coordinate geometry and translation transformations. Suitable for students in Grades 6-8.

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