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 $(4, -1)$.

Would you like further details or have any questions?

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.