https://file.aiquickdraw.com/mathbot/file/1729646595693c1d4zg0m.jpg

The image shows a rotation task where you're asked to determine the coordinates of point D' after a 90° rotation. The original coordinates of D are given as \( D(5, -1) \).

### 90° Rotation Rule:
- **Clockwise**: The rule for a 90° clockwise rotation around the origin is \( (x, y) \to (y, -x) \).
- **Counterclockwise**: The rule for a 90° counterclockwise rotation is \( (x, y) \to (-y, x) \).

Since the image doesn't specify the direction, I will assume it's counterclockwise, which is most common unless otherwise stated.

#### Applying the 90° Counterclockwise Rotation to \( D(5, -1) \):
Using the rule \( (x, y) \to (-y, x) \), we get:
- \( D(5, -1) \to D'(-(-1), 5) = D'(1, 5) \).

Thus, the coordinates of \( D' \) are \( \boxed{(1, 5)} \), matching the third option.

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. How would the coordinates change if the rotation was 90° clockwise?
2. What is the effect of a 180° rotation on any point?
3. How do you rotate a point 270° counterclockwise?
4. Can you apply the rotation rule to point A(4, -1)?
5. How does the distance from the origin affect the result of a rotation?

**Tip:** When rotating points, always pay attention to the direction and whether the rotation is around the origin or another point.

Graph the preimage and image of each rotation. Determine the coordinates of D'.

Learn how to determine the coordinates of a point after a 90° rotation around the origin. This problem covers key geometry concepts related to rotations on the coordinate plane, including the formulas for 90° clockwise and counterclockwise rotations.

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