To determine if the provided coordinates for $C'$ are correct after a 90-degree counterclockwise rotation, let's analyze the original point $C$ and perform the rotation.

Original Point

The original coordinates for point $C$ are given as $(0, 3)$.

90-Degree Counterclockwise Rotation

For a 90-degree counterclockwise rotation around the origin, the transformation rules for the coordinates are:

• If the original point is $(x, y)$, the new point $(x', y')$ after the rotation will be $(-y, x)$.

Applying these rules to point $C$:

• Original coordinates of $C$: $(0, 3)$
• Rotated coordinates for $C'$: $(-3, 0)$

Given Answer Analysis

The given coordinates for $C'$ are $(0, -3)$.

Conclusion

There is an error in the given answer. After a 90-degree counterclockwise rotation, the coordinates for $C'$ should be $(-3, 0)$ and not $(0, -3)$.

Would you like more details on this problem, or do you have any other questions?

Here are some related questions you might find interesting:

1. How do you perform a 180-degree rotation on a coordinate plane?
2. What are the general rules for rotating a point 270 degrees counterclockwise?
3. Can you explain the effect of different rotation angles on coordinates?
4. How do you determine the center of rotation for a set of points?
5. What is the difference between clockwise and counterclockwise rotations in coordinate transformations?

Tip: When performing coordinate transformations, it's helpful to visualize or sketch the points on a graph to see the effects of the transformation clearly.