https://file.aiquickdraw.com/mathbot/file/1727454102432h0ic2pxa.jpg

We are given the translation rule \((x, y) \to (x - 3, y + 2)\), and we need to apply this rule to each of the preimage coordinates to find the corresponding image coordinates.

Here’s how to proceed:

1. **For (0, 1):**
   \[
   x' = 0 - 3 = -3
   \]
   \[
   y' = 1 + 2 = 3
   \]
   So, the image coordinate is \((-3, 3)\).

2. **For (2, 3):**
   \[
   x' = 2 - 3 = -1
   \]
   \[
   y' = 3 + 2 = 5
   \]
   So, the image coordinate is \((-1, 5)\).

3. **For (4, 2):**
   \[
   x' = 4 - 3 = 1
   \]
   \[
   y' = 2 + 2 = 4
   \]
   So, the image coordinate is \((1, 4)\).

### Final Image Coordinates:
- For (0, 1) → (-3, 3)
- For (2, 3) → (-1, 5)
- For (4, 2) → (1, 4)

Would you like more details or explanations about any part of this? Here are 5 related questions to expand on this:

1. What is the general form of a translation in the coordinate plane?
2. How would you describe the effect of the rule \((x, y) \to (x - 3, y + 2)\) on any shape?
3. Can translations change the size or orientation of a shape?
4. How would you reverse this translation? What would the rule be?
5. How can you check if the translation was applied correctly?

**Tip**: Always check the sign changes and arithmetic carefully when applying translation rules to avoid small errors!

The coordinates of a triangle are given in the table. The triangle is translated using the rule (x, y) → (x - 3, y + 2). What are the coordinates of the image of the triangle?

Learn how to find the image coordinates of a triangle after translation using the rule (x, y) → (x - 3, y + 2). This problem involves coordinate geometry and applying translation formulas. Suitable for students in Grades 6-8.

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