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To solve this problem, we need to reflect point \( C(3, -9) \) over the line \( y = x \). The rule for reflecting a point \( (x, y) \) over the line \( y = x \) is to swap the coordinates, meaning the point \( (x, y) \) becomes \( (y, x) \).

For point \( C(3, -9) \), reflecting over the line \( y = x \) gives us:

\[
C' = (-9, 3)
\]

Thus, the coordinates of the reflected point are \( (-9, 3) \).

The correct answer is **B. \( (-9, 3) \)**.

Would you like further explanation or details? Here are five related questions to enhance your understanding:

1. How do you reflect a point over the line \( y = -x \)?
2. What is the rule for reflecting points over the x-axis or y-axis?
3. How would you calculate the reflection of a point over a different line, such as \( y = 2x + 1 \)?
4. How can you determine if two figures are congruent after a reflection?
5. What are some practical applications of geometric reflections in real-world scenarios?

**Tip:** Remember that reflecting over the line \( y = x \) always involves swapping the x- and y-coordinates.

Coach Nelson is designing a new park that will have both a baseball diamond and a softball diamond. The baseball diamond will have the same dimensions as the softball diamond. The position of the baseball diamond will be determined by the reflection of the image of the softball diamond about the line y = x. What are the coordinates of the reflected image of point C(3, -9)?

This problem covers the reflection of a point over the line y = x in coordinate geometry. Learn how to reflect point C(3, -9) to find the new coordinates, focusing on the reflection theorem. Suitable for Grades 8-10.

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