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.