https://file.aiquickdraw.com/mathbot/file/172571814577775w13bpu.jpg

The problem asks for the coordinates of the vertices of the quadrilateral after a **180° counterclockwise rotation** around the origin. Let's analyze the vertices and apply the transformation.

### Step 1: Identify the Coordinates of the Original Vertices
From the image, the coordinates of the vertices of the quadrilateral \( RSTQ \) appear to be:
- \( R(7, 9) \)
- \( S(9, 9) \)
- \( T(9, 5) \)
- \( Q(7, 5) \)

### Step 2: Apply the 180° Counterclockwise Rotation
A 180° counterclockwise rotation around the origin transforms any point \( (x, y) \) to \( (-x, -y) \). Applying this to each vertex:

- \( R(7, 9) \) becomes \( R'(-7, -9) \)
- \( S(9, 9) \) becomes \( S'(-9, -9) \)
- \( T(9, 5) \) becomes \( T'(-9, -5) \)
- \( Q(7, 5) \) becomes \( Q'(-7, -5) \)

### Step 3: New Coordinates After Rotation
The new coordinates of the vertices after the 180° counterclockwise rotation are:
- \( R'(-7, -9) \)
- \( S'(-9, -9) \)
- \( T'(-9, -5) \)
- \( Q'(-7, -5) \)

Let me know if you'd like more details or clarifications! Here are some related questions to deepen your understanding:

1. What is the rule for rotating points 90° counterclockwise around the origin?
2. How would the coordinates change if the rotation were 90° clockwise instead of 180°?
3. What is the general formula for rotating a point around the origin by any angle \( \theta \)?
4. How can you reflect a shape over the y-axis, and what happens to the coordinates?
5. Can you explain how to perform a translation of a shape in addition to a rotation?

**Tip:** When rotating shapes on a coordinate plane, always remember that counterclockwise rotations are positive, and clockwise rotations are negative in terms of angle measures.

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

Learn how to perform a 180° counterclockwise rotation on a quadrilateral in a coordinate plane. The problem covers key concepts in geometry and transformations, suitable for students in Grades 6-8. Detailed explanation of the rule (x, y) becomes (-x, -y) for rotation.

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