onsider the ordered pair G(-2,-5). Determine the ordered pair for G' after a rotation of each of the following counterclockwise rotations:

90 180 270 360 

To determine the coordinates of point \( G' \) after rotating the point \( G(-2, -5) \) counterclockwise by 90°, 180°, 270°, and 360°, we use the following rules for rotation about the origin:

1. **90° Rotation (Counterclockwise):**
   - Formula: \( (x, y) \) → \( (-y, x) \)
   - For \( G(-2, -5) \):  
     \( G' = (-(-5), -2) = (5, -2) \)

2. **180° Rotation (Counterclockwise):**
   - Formula: \( (x, y) \) → \( (-x, -y) \)
   - For \( G(-2, -5) \):  
     \( G' = (-(-2), -(-5)) = (2, 5) \)

3. **270° Rotation (Counterclockwise):**
   - Formula: \( (x, y) \) → \( (y, -x) \)
   - For \( G(-2, -5) \):  
     \( G' = (-5, 2) \)

4. **360° Rotation (Counterclockwise):**
   - Formula: \( (x, y) \) → \( (x, y) \) (No change in position)
   - For \( G(-2, -5) \):  
     \( G' = (-2, -5) \)

**Summary of results:**
- After 90° rotation: \( G'(5, -2) \)
- After 180° rotation: \( G'(2, 5) \)
- After 270° rotation: \( G'(-5, 2) \)
- After 360° rotation: \( G'(-2, -5) \)

Would you like a detailed explanation of how each transformation is derived, or do you have any other questions?

Here are 5 related questions to expand on this information:
1. What is the effect of rotating a point 90° clockwise around the origin?
2. How would you reflect the point \( G(-2, -5) \) across the x-axis?
3. What are the coordinates of point \( G(-2, -5) \) after a reflection over the y-axis?
4. How does a 180° rotation differ from a reflection across the origin?
5. How would you determine the coordinates after rotating around a point other than the origin?

**Tip:** When rotating points around the origin, always keep in mind the rules for how x and y coordinates switch places and change signs for each specific angle of rotation.

Consider the ordered pair G(-2,-5). Determine the ordered pair for G' after a rotation of each of the following counterclockwise rotations: 90, 180, 270, 360

Learn how to determine the coordinates of point G(-2, -5) after counterclockwise rotations by 90°, 180°, 270°, and 360°. This problem covers key concepts in geometry and coordinate geometry, including the rotation theorems about the origin. Suitable for students in Grades 8-10.

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