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To determine the coordinates of point \( C \) from the given problem, we need to follow the steps of applying the symmetry transformations.

1. **Symmetry of Point \( A(p, q) \) with respect to the line \( y = q - 3 \)**:

   - The equation of the line is \( y = q - 3 \).
   - The point \( A \) has coordinates \( (p, q) \).
   - We need to find the coordinates of point \( B \) after applying the symmetry.

   The symmetry of point \( A \) with respect to a line involves finding the perpendicular distance to the line and reflecting it. 

   For the line \( y = q - 3 \) and point \( A(p, q) \), the symmetrical point \( B \) will have coordinates \( (p, 6 - q) \).

2. **Symmetry of Point \( C \) with respect to the x-axis**:

   - We apply symmetry to point \( B \) with respect to the x-axis. Reflecting \( B \) about the x-axis changes the y-coordinate to its negative value while keeping the x-coordinate the same.

   - For point \( B (p, 6 - q) \), the symmetry with respect to the x-axis gives point \( C \) with coordinates \( (p, q - 6) \).

Given the choices, the correct coordinates of \( C \) are:

\[ \boxed{C} (p, q - 6) \]

So, the answer is \( \text{C) } (p, q - 6) \).

Would you like further details or have any questions about the solution? Here are some related questions:

1. How do you derive the formula for the reflection of a point across a line?
2. Can you show the steps to find the intersection point of a line and its perpendicular from a given point?
3. How do transformations affect the coordinates of geometric points?
4. What are the properties of symmetry in a coordinate plane?
5. How can you verify the reflection of a point mathematically?

**Tip:** When dealing with symmetry problems, always break down the transformations step-by-step to avoid errors and ensure accuracy.

En el plano cartesiano, al punto A(p, q), con p > 0 y q > 6, se le aplica una simetría respecto a la recta de ecuación y = q - 3, obteniéndose un punto B. Si a un punto C se le aplica una simetría respecto al eje X y se obtiene el punto B, entonces las coordenadas de C son:

Learn how to solve a problem involving symmetry and reflections in the Cartesian plane. The problem involves reflecting a point across a line and the x-axis to find new coordinates. Suitable for high school students.

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