rotate 180 counterclockwise about the origin -4,1

To rotate a point \( (-4, 1) \) 180° counterclockwise about the origin, we need to follow the general rule for a 180° rotation around the origin, which states:

1. **For any point** \((x, y)\), rotating it 180° around the origin will transform it to the point \((-x, -y)\).
   
   Therefore, for the point \( (-4, 1) \):
   
   \[
   (-4, 1) \rightarrow (4, -1)
   \]

2. **Result**: After rotating \( (-4, 1) \) 180° counterclockwise about the origin, the new coordinates are \( (4, -1) \).

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### Related Questions:
1. What is the rule for rotating a point 90° counterclockwise about the origin?
2. How would a 270° counterclockwise rotation affect the point \( (-4, 1) \)?
3. What is the difference between rotating 180° clockwise and counterclockwise around the origin?
4. How can we verify the accuracy of a 180° rotation transformation?
5. What are other transformations that can move a point to the coordinates \( (4, -1) \)?

**Tip:** When rotating points, remember that a 180° rotation gives the same result clockwise and counterclockwise because it ends up on the exact opposite side of the origin.

Learn how to rotate the point (-4, 1) 180 degrees counterclockwise about the origin using the rotation transformation formula. Understand the steps to find the new coordinates after rotation, suitable for high school students in Grades 9-10.

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