https://file.aiquickdraw.com/mathbot/file/1726186587307cji59ajp.jpg

What is the correct option?
A rotation 90° counterclockwise about the origin

A translation 1 unit to the left and 9 units up

A rotation 90° clockwise about the origin

A translation 1 unit to the right and 9 units down

From the image, Figure \( G \) is the result of a transformation on Figure \( F \). Let's analyze the transformations:

- **Figure \( F \)** is located below the x-axis (in the third quadrant), while **Figure \( G \)** is above the x-axis (in the second quadrant).
- **Rotation**: Since Figure \( F \) is reflected across the x-axis and appears to have rotated from its original position, the correct transformation seems to be a **rotation**.

### Check the options:

1. **A rotation 90° counterclockwise about the origin**:
   - This would place the figure from quadrant III to quadrant II, which matches the movement of Figure \( F \) to Figure \( G \).
   
2. **A translation 1 unit to the left and 9 units up**:
   - This is a vertical and horizontal shift, but it wouldn't account for the rotation of the figure.

3. **A rotation 90° clockwise about the origin**:
   - A clockwise rotation would place the figure in quadrant IV, which is incorrect.

4. **A translation 1 unit to the right and 9 units down**:
   - Again, this only shifts the figure but does not rotate it.

### Conclusion:
The correct transformation is **a 90° counterclockwise rotation about the origin**.

Would you like further details or have additional questions? Here are some related questions to explore:

1. How can you confirm a 90° counterclockwise rotation on a coordinate plane?
2. What are the properties of rotation about the origin in geometry?
3. How do you find the image of a point after a 90° counterclockwise rotation?
4. What is the difference between rotation and reflection in transformations?
5. How do translations affect coordinates compared to rotations?

**Tip**: When rotating a figure counterclockwise by 90° around the origin, switch the coordinates \((x, y)\) to \((-y, x)\).

Figure G is the result of a transformation on Figure F. Which transformation would accomplish this?

Discover how to identify a 90° counterclockwise rotation on a coordinate plane. This example explores how Figure F transforms into Figure G using the properties of rotation. Suitable for students in Grades 8-10.

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