https://file.aiquickdraw.com/mathbot/file/1725539116840kdvtdqlz.jpg

The problem involves determining the image of point \( Q \) after it is rotated by \( -150^\circ \) around a center of rotation that is clearly marked on the diagram. The negative angle indicates a clockwise rotation.

### Steps to Solve:
1. **Identify the center of rotation:** It's the black dot labeled "Center" in the middle of the diagram.
2. **Locate point \( Q \):** \( Q \) is marked as a blue dot.
3. **Visualize a \( -150^\circ \) (clockwise) rotation:** Starting from \( Q \), we need to rotate \( Q \) in the clockwise direction around the center by \( 150^\circ \). 

   Based on a rough visual estimate of \( 150^\circ \), the image of \( Q \) should land near one of the labeled points (A, B, C, or D).

### Analysis:
Looking at the relative positions, the point that seems to match a \( 150^\circ \) clockwise rotation is **point C**, as it aligns with the direction of a large clockwise angle from \( Q \).

### Answer:
The image of point \( Q \) after a \( -150^\circ \) rotation appears to be point **C**.

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Would you like further clarification on rotation transformations? Here are 5 related questions for further practice:
1. How do you determine the angle of rotation in a counterclockwise direction?
2. What is the difference between clockwise and counterclockwise rotations?
3. How can you rotate a point using trigonometric functions?
4. What is the image of a point under a \( 90^\circ \) counterclockwise rotation?
5. How can you find the coordinates of a rotated point without a graph?

**Tip:** For precise rotations, try sketching smaller intermediate angles (like \( 90^\circ \)) to help visualize the full rotation more clearly.

Which point is the image of Q after a -150° rotation around the indicated center of rotation?

Solve the problem of rotating point Q by -150° around a fixed center. Understand the key geometric concepts and transformations used in this process, including the rotation formula and the Rotation Theorem. This is ideal for students in Grades 9-10.

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