What is the rule for a 180° clockwise rotation?Question 17Select one:a.(x, y) → (-y, -x)b.(x, y) → (y, x)c.(x, y) → (y, -x) d.(x, y) → (-x, -y)

1. Break Down the Problem

To determine the rule for a 180° clockwise rotation in the coordinate plane, we need to analyze how points transform when rotated 180° about the origin.

2. Relevant Concepts

When a point $(x, y)$ is rotated 180° clockwise around the origin, each coordinate $x$ and $y$ changes its sign.

3. Analysis and Detail

• The original point is $(x, y)$.
• Applying a 180° clockwise rotation to the point $(x, y)$:
  • The x-coordinate, originally $x$, moves to the opposite side of the origin: it becomes $-x$.
  • The y-coordinate, originally $y$, also moves to the opposite side: it becomes $-y$.

This transformation can be expressed mathematically as: $(x, y) \rightarrow (-x, -y)$

4. Verify and Summarize

The transformation rule for a 180° clockwise rotation is indeed $(x, y) \rightarrow (-x, -y)$.

Final Answer

The correct answer is: d. $(x, y) \rightarrow (-x, -y)$.