https://file.aiquickdraw.com/mathbot/file/1733938660695razwh5cs.jpg

Thanks for sharing the file! Let’s analyze the tasks given in this geometry exercise.

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### Key Exercises:
1. **Exercise 5:** Rotate the line segment \( A(-3, 2) \) and \( B(-1, 2) \) **90° about \( P(-2, 0) \)**.  
   - **Steps**:
     1. Translate \( P(-2, 0) \) to the origin by subtracting its coordinates from \( A \) and \( B \).
     2. Perform a 90° counterclockwise rotation around the origin using the rule:  
        \( (x, y) \to (-y, x) \).
     3. Translate back by adding \( P(-2, 0) \)'s coordinates to the result.

2. **Exercise 6:** Rotate \( Q(1, 1) \) and \( R(1, -2) \) **180° about \( P(1, 2) \)**.  
   - **Steps**:
     1. Translate \( P(1, 2) \) to the origin.
     2. Apply a 180° rotation using the rule:  
        \( (x, y) \to (-x, -y) \).
     3. Translate back.

3. **Exercise 7:** A combination of transformations is applied to the line segment \( XY \) with endpoints \( X(-3, 1) \) and \( Y(4, -5) \):  
   - **Rotation (180° counterclockwise about origin)**.
   - **Translation (x, y) → (x − 1, y + 1)**.  
     Apply these transformations sequentially.

4. **Exercise 8:** A composition of:  
   - Reflection over the line \( y = x \): Swap the coordinates:  
     \( (x, y) \to (y, x) \).  
   - Rotation (180° clockwise about origin).

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Would you like me to work through specific problems and graph the solutions? If so, let me know which one you'd like me to begin with! 😊

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### Related Questions:
1. How do coordinate transformations change with respect to different centers of rotation?
2. What is the general rule for a 90° clockwise rotation around any point?
3. How does reflecting over the line \( y = x \) affect points with integer coordinates?
4. What are the effects of combining translations with rotations in sequences?
5. How can we confirm a point's location after multiple transformations?

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### Tip:
Always verify your final coordinates by substituting them back into the transformation rules—this ensures precision!

Graph the line segments and their images after specific transformations. Tasks include rotating line segments by 90° or 180° around a given point, reflecting across y = x, and combining transformations such as rotations and translations.

Explore how to graph line segments and their transformations, including rotations, reflections, and translations in the coordinate plane. This exercise covers essential concepts and rules in geometry for high school students.

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