https://file.aiquickdraw.com/mathbot/file/17256413539940jaruf9b.jpg

In the provided image, triangle \( RST \) is translated to form triangle \( R'S'T' \). The problem states that the triangle is translated 6 units to the left and 4 units up. We are asked to determine which rule best describes this transformation from the choices given.

### Translation Process:
- Moving 6 units to the left means subtracting 6 from the \( x \)-coordinate.
- Moving 4 units up means adding 4 to the \( y \)-coordinate.

### General Rule for Translation:
The rule for translating any point \( (x, y) \) is given by:
\[
(x', y') = (x - 6, y + 4)
\]
This means the \( x \)-coordinate is decreased by 6, and the \( y \)-coordinate is increased by 4.

### Matching the Answer Choices:
- **A**: \( (x, y) \rightarrow (6x, -4y) \) - This is not a translation rule.
- **B**: \( (x, y) \rightarrow (-6x, 4y) \) - Incorrect as it alters the coordinates through scaling, not translation.
- **C**: \( (x, y) \rightarrow (x - 6, y - 4) \) - This is incorrect because it translates both coordinates downward.
- **D**: \( (x, y) \rightarrow (x - 6, y + 4) \) - This correctly translates 6 units to the left and 4 units up.

### Conclusion:
The correct answer is **D**.

Would you like further details on translation transformations, or do you have any questions?

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Here are five related questions for further practice:
1. What is the rule for translating a shape 3 units to the right and 5 units down?
2. How would you describe the transformation if the triangle was reflected over the \( y \)-axis?
3. What happens to the coordinates of a point when translated 8 units to the right and 2 units down?
4. How do you determine if a transformation is a rotation instead of a translation?
5. What effect does translating an object diagonally by equal units in both directions have on its orientation?

**Tip:** In translation, the object moves without rotating or resizing, and every point shifts the same distance in the same direction.

Triangle RST is translated 6 units to the left and 4 units up to create triangle R'S'T'. Which rule best describes this transformation?

Understand how to translate triangle RST by 6 units to the left and 4 units up on a coordinate plane. This problem highlights geometric translations and the transformation rule (x', y') = (x - 6, y + 4), suitable for students in Grades 6-8.

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