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In this problem, the triangle \( RST \) is rotated 270° counterclockwise about the origin to form triangle \( R'S'T' \). We need to determine the correct transformation rule for this rotation.

### Rotation Rules in Coordinate Geometry
When rotating a point \((x, y)\) about the origin, the general transformation rules for common counterclockwise rotations are as follows:
- 90°: \((x, y) \rightarrow (-y, x)\)
- 180°: \((x, y) \rightarrow (-x, -y)\)
- 270°: \((x, y) \rightarrow (y, -x)\)

### Applying the 270° Rotation Rule
From the rules above, for a 270° counterclockwise rotation, the transformation should be:
\[
(x, y) \rightarrow (y, -x)
\]
This corresponds to option **D** in the question.

### Answer:
The correct rule for the 270° counterclockwise rotation is **D**: \((x, y) \rightarrow (y, -x)\).

Do you have any questions or would you like more details?

### Related Questions:
1. What is the rule for a 90° counterclockwise rotation?
2. How would a 180° counterclockwise rotation affect the coordinates of a point?
3. Can you explain the difference between clockwise and counterclockwise rotations?
4. How would you apply the 270° rule to a specific point, say \((3, 4)\)?
5. What is the geometric significance of rotating objects in the coordinate plane?

### Tip:
Always visualize rotations as movement around the origin in the coordinate plane to ensure you apply the correct transformation rule.

Triangle RST is rotated 270° counterclockwise about the origin of a coordinate plane to create triangle R'S'T'. Which rule describes this transformation?

Learn how to determine the transformation rule for a 270° counterclockwise rotation in coordinate geometry. The problem involves key concepts like transformation rules and rotations, making it suitable for students in Grades 8-10.

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