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Determine the coordinates for C' after a 90 degree rotation counterclockwise. The coordinates for C' are (0,-3). The coordinates for the original point, C, are (0,3)

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.

Explore how to correct coordinates after a 90-degree counterclockwise rotation in coordinate geometry. This problem discusses rotation transformations around the origin, analyzing point C and its rotated position. Suitable for Grades 6-8 students learning about coordinate transformations.

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