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.