To solve this problem, we need to perform a 90-degree rotation on point $C$ with coordinates $(3, 6)$.

90-Degree Rotation Rules

For a 90-degree rotation:

1. Counterclockwise Rotation (which is generally the default in math unless stated otherwise):
   • The new coordinates $(x', y')$ of a point $(x, y)$ are $(-y, x)$.
2. Clockwise Rotation:
   • The new coordinates $(x', y')$ of a point $(x, y)$ are $(y, -x)$.

Let's assume the problem requires a counterclockwise rotation (which is the typical convention for positive angles):

1. Starting with $C(3, 6)$:
   • Apply the rule: $(-y, x)$.
   • Substitute the coordinates: $(-6, 3)$.

Thus, the new coordinates of point $C$ after a 90-degree counterclockwise rotation are $(-6, 3)$.

The correct answer is:

• $(-6, 3)$

Would you like further details or have any questions?

Here are some related questions that may interest you:

1. What are the rotation rules for 180 and 270 degrees?
2. How would the result change if the rotation were clockwise instead of counterclockwise?
3. What are the effects of rotating a point by 360 degrees?
4. How can I perform a reflection over the x-axis or y-axis?
5. Can you explain the general formula for rotating a point about any arbitrary point?

Tip: Remember, rotating points 90 degrees counterclockwise swaps the coordinates and changes the sign of the new x-coordinate.