What is the image of the point left parenthesis, minus, 1, comma, 9, right parenthesis(−1,9) after a rotation of 180, degrees180 
∘
  counterclockwise about the origin?

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.

What is the image of the point (−1,9) after a rotation of 180° counterclockwise about the origin?

Learn how to find the image of the point (-1,9) after a 180° counterclockwise rotation about the origin. This solution covers key concepts in coordinate geometry, including the rotation formula. Suitable for students in Grades 8-10.

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