To determine the correct transformation rule for a 270° clockwise rotation about the origin, let's analyze the effect of the rotation on a point $(x, y)$ on the coordinate plane.

Rotation Rules:

1. 90° clockwise rotation: $(x, y) \to (y, -x)$
2. 180° rotation: $(x, y) \to (-x, -y)$
3. 270° clockwise rotation (equivalent to 90° counterclockwise): $(x, y) \to (-y, x)$

Rule for 270° Clockwise Rotation:

For a 270° clockwise rotation, the $x$-coordinate becomes the opposite of the $y$-coordinate, and the $y$-coordinate becomes the $x$-coordinate. Thus, the transformation is:

$(x, y) \to (-y, x)$

Correct Answer:

C. $(x, y) \to (-y, x)$

Would you like a detailed example or visualization of this? Let me know! 😊

---

Related Questions:

1. What are the rules for 90°, 180°, and 360° rotations about the origin?
2. How would the transformation change for counterclockwise rotations?
3. Can you determine the transformation for a 270° clockwise rotation of a specific triangle (e.g., $(2, 3)$, $(-1, 4)$, $(0, -5)$)?
4. How does a reflection differ from a rotation in terms of transformations?
5. What happens if the triangle is rotated 270° clockwise about a different point instead of the origin?

Tip:

When solving rotation problems, sketch the original point or figure and rotate it step by step to ensure the transformation is applied correctly.