The problem asks for the image of point $A(9, 0)$ after being reflected over the line $y = -x$.

Reflection over the line $y = -x$

To reflect a point $(x, y)$ over the line $y = -x$, the coordinates transform as follows: $(x, y) \rightarrow (-y, -x)$

Applying this to $A(9, 0)$:

For point $A(9, 0)$, using the transformation rule: $(9, 0) \rightarrow (0, -9)$

Thus, the image of point $A(9, 0)$ after reflection is $(0, -9)$.

Answer:

The correct choice is C. $(0, -9)$.

Would you like more details or have any questions about this reflection process?

Related questions:

1. How do you reflect a point over the line $y = x$?
2. What is the geometric interpretation of reflecting over the line $y = -x$?
3. How would the point $(-3, 7)$ be reflected over the line $y = -x$?
4. How does reflection over the $x$-axis compare with reflection over the line $y = -x$?
5. What is the equation of a line that reflects points symmetrically about the origin?

Tip:

When reflecting over the line $y = -x$, remember that both coordinates are swapped and their signs are reversed!