https://file.aiquickdraw.com/mathbot/file/1729379415790m3xlcqii.jpg

To solve this problem, let’s walk through how to find the new coordinates after rotating the given points 270° counterclockwise about the origin. 

### **Key Concept: Rotation by 270° Counterclockwise**
- A **270° counterclockwise rotation** transforms a point \((x, y)\) to \((y, -x)\).

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Now, let's extract the vertices from the graph shown in your image:

1. **Point R**: \((-2, 3)\)
2. **Point S**: \((-4, 1)\)
3. **Point T**: \((-1, -1)\)
4. **Point U**: \((-3, -4)\)

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### **Rotation Calculation: 270° Counterclockwise**
Using the transformation rule \((x, y) \rightarrow (y, -x)\):

- **R(-2, 3)** → \( (3, 2) \)
- **S(-4, 1)** → \( (1, 4) \)
- **T(-1, -1)** → \( (-1, 1) \)
- **U(-3, -4)** → \( (-4, 3) \)

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### **New Coordinates after 270° Counterclockwise Rotation**
- **R'**: \( (3, 2) \)
- **S'**: \( (1, 4) \)
- **T'**: \( (-1, 1) \)
- **U'**: \( (-4, 3) \)

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Let me know if you need more details or if anything is unclear!

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### 5 Related Questions:
1. What is the general formula for 90° and 180° rotations?
2. How do clockwise and counterclockwise rotations differ?
3. How do rotations affect the orientation of a shape?
4. What are other transformations besides rotations (e.g., translations, reflections)?
5. How would the coordinates change if the rotation was around a different point instead of the origin?

**Tip:** For easier rotation of coordinates, remember that a 270° counterclockwise rotation is equivalent to a 90° clockwise rotation.

Write the coordinates of the vertices after a rotation 270° counterclockwise around the origin.

Learn how to determine the new coordinates of vertices after a 270° counterclockwise rotation about the origin. This problem explains the (x, y) → (y, -x) transformation with a detailed example. Suitable for students in Grades 8-10.

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