To find the image of the point $(-1, 9)$ after a 180° counterclockwise rotation about the origin, we can apply the standard rotation rule for 180° about the origin:

$(x, y) \rightarrow (-x, -y)$

Step-by-step:

1. The original point is $(-1, 9)$.
2. Applying the rotation rule, we change the signs of both coordinates: $(-1, 9) \rightarrow (1, -9)$

Thus, the image of the point $(-1, 9)$ after a 180° counterclockwise rotation about the origin is $(1, -9)$.

Would you like more details or have any further questions?

Here are 5 related questions:

1. What is the image of the point $(3, -2)$ after a 90° counterclockwise rotation about the origin?
2. How would the point $(4, 5)$ change after a 270° clockwise rotation about the origin?
3. What is the image of the point $(2, -6)$ after a reflection over the x-axis?
4. How does a 360° rotation affect any point in the coordinate plane?
5. What are the coordinates of the point $(7, 8)$ after a rotation of 180° followed by a reflection over the y-axis?

Tip: Rotating points 180° about the origin always results in the coordinates changing their signs.