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Which of the following would be a rule for rotating 90 degrees clockwise? A. (x, y) → (-x, y) B. (x, y) → (y, -x) C. (x, y) → (-x, -y) D. (x, y) → (-y, x)
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Answer

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Step 1:
Let's solve this step by step:

Step 2:
: Understand the Rotation Transformation

A 90 -degree clockwise rotation means we need to transform the coordinates (x, y) to a new position that represents a quarter turn clockwise around the origin.

Step 3:
: Analyze Each Option

Let's visualize what happens to a point (x, y) when rotated 90 degrees clockwise: - The x-coordinate will change - The y-coordinate will change - The point will move to a new quadrant

Step 4:
: Test Each Option

D. $$(x, y) \rightarrow (-y, x)
This is a reflection across the y-axis, not a rotation. This is a 90 -degree counterclockwise rotation, not clockwise. This is a 180 -degree rotation, not 90 degrees. This represents a 90 -degree clockwise rotation.

Step 5:
: Verify Option D

- Rotated point: $$(-3, 2)
Let's confirm with an example point (2, 3): This confirms a 90 -degree clockwise rotation.

Final Answer

D. (x, y) \rightarrow (-y, x) is the correct rule for rotating 90 degrees clockwise.