Question

The coordinates for a point and its image are Q(−3,−5)
and Q′(5,−3)
. Based on the mapping rules for rotations, which transformation occurred?(1 point)
Responses

a 90-degree (counterclockwise) rotation
a 90-degree (counterclockwise) rotation

a 270-degree (counterclockwise) rotation
a 270-degree (counterclockwise) rotation

a −180
-degree (clockwise) rotation or a 180-degree (counterclockwise) rotation
a negative 180 -degree (clockwise) rotation or a 180-degree (counterclockwise) rotation

a −90
-degree (clockwise) rotation

Answer 1

To determine the rotation that occurred from the point \( Q(-3, -5) \) to its image \( Q'(5, -3) \), we can analyze the coordinates.

1. **Original Point**: \( Q(-3, -5) \)
2. **Image Point**: \( Q'(5, -3) \)

### Analysis of the Transformation:
- A 90-degree counterclockwise rotation around the origin changes a point \( (x, y) \) to \( (-y, x) \).
- A 270-degree counterclockwise rotation (or 90 degrees clockwise) changes a point \( (x, y) \) to \( (y, -x) \).
- A 180-degree rotation (both clockwise and counterclockwise) changes a point \( (x, y) \) to \( (-x, -y) \).

### Testing Different Rotations:
1. **90-degree counterclockwise rotation**:
- For \( Q(-3, -5) \):
\[
(-(-5), -3) = (5, -3) \quad \text{(which is } Q'\text{)}
\]

2. **270-degree counterclockwise rotation**:
- For \( Q(-3, -5) \):
\[
(-5, 3) = (-5, 3) \quad \text{(not equal to } Q'\text{)}
\]

3. **180-degree rotation**:
- For \( Q(-3, -5) \):
\[
(3, 5) \quad \text{(not equal to } Q'\text{)}
\]

4. **90-degree clockwise rotation**:
- For \( Q(-3, -5) \):
\[
(-5, 3) \quad \text{(not equal to } Q'\text{)}
\]

### Conclusion:
The transformation that occurred is a **90-degree counterclockwise rotation**.

Therefore, the correct response is:

**a 90-degree (counterclockwise) rotation**.