https://file.aiquickdraw.com/mathbot/file/17257178536996t1c7wut.jpg

The problem asks for the coordinates of the vertices after a 180° counterclockwise rotation around the origin. Here's how to solve it:

### Step-by-step explanation:
1. **Rule for 180° Counterclockwise Rotation**:
   When you rotate a point \((x, y)\) by 180° counterclockwise around the origin, the new coordinates will be \((-x, -y)\). This is because a 180° rotation flips both the x- and y-coordinates.

2. **Identify the coordinates of the original vertices** (from the graph):
   - \( R = (9, 8) \)
   - \( S = (12, 8) \)
   - \( T = (12, 4) \)
   - \( Q = (9, 4) \)

3. **Apply the rotation rule**:
   - For \( R(9, 8) \), the new coordinates will be \( (-9, -8) \).
   - For \( S(12, 8) \), the new coordinates will be \( (-12, -8) \).
   - For \( T(12, 4) \), the new coordinates will be \( (-12, -4) \).
   - For \( Q(9, 4) \), the new coordinates will be \( (-9, -4) \).

### Final coordinates after rotation:
- \( R' = (-9, -8) \)
- \( S' = (-12, -8) \)
- \( T' = (-12, -4) \)
- \( Q' = (-9, -4) \)

Let me know if you'd like further explanation or have any questions!

Here are 5 related questions to explore:
1. What would the coordinates be after a 90° counterclockwise rotation?
2. How would the graph look after a 270° clockwise rotation?
3. What is the general rule for rotating points by 180° clockwise?
4. How does the distance between points change after a 180° rotation?
5. What are the transformations involved in a reflection over the origin?

**Tip:** When performing a rotation, always pay attention to the center of rotation (origin or any other point) and the angle (90°, 180°, etc.) to apply the correct transformation.

Write the coordinates of the vertices after a rotation 180° counterclockwise around the origin.

Learn how to determine the coordinates of a shape's vertices after a 180° counterclockwise rotation around the origin. This problem covers key geometric concepts, including the transformation rule for rotations. Suitable for students in Grades 8-10.

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