To determine the correct transformation rule, we need to analyze the coordinates of the pre-image point $P$ and its corresponding image point on the coordinate grid.

Here’s how to approach the problem:

1. Identify the coordinates of the pre-image point $P$. Let's denote them as $(x, y)$.
2. Identify the coordinates of the image of point $P$. Let's denote them as $(x', y')$.
3. Compare $(x, y)$ and $(x', y')$ to determine the relationship and match it with one of the transformation rules.

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Explanation of Transformation Rules:

1. Option A: $(x, y) \to (-y, x)$:

   • This is a 90° counterclockwise rotation around the origin.

2. Option B: $(x, y) \to (-x, y)$:

   • This is a reflection over the y-axis.

3. Option C: $(x, y) \to (-y, -x)$:

   • This is a 180° rotation around the origin.

4. Option D: $(x, y) \to (y, -x)$:

   • This is a 90° clockwise rotation around the origin.

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Steps to Solve:

• Provide the coordinates of the points $P$ (pre-image) and $P'$ (image) from the grid. If you share the image or provide the points, I will verify the transformation.

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Would you like to provide the coordinates or upload the image for a detailed analysis?

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Related Questions:

1. How do you determine transformations using matrix operations?
2. What is the effect of combining two rotations on a coordinate plane?
3. How do you derive transformation rules for reflections?
4. What is the general form of a rotation matrix?
5. How can a geometric transformation be reversed?

Tip: Always check the orientation of the axes and the signs of the coordinates after the transformation. It helps in quickly identifying the type of transformation.