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?
A. a 270-degree (counterclockwise) rotation
B. a reflection across the x-axis
C. a 90-degree (counterclockwise) rotation
D. a 180-degree rotation

Answer 1

To determine which transformation occurred to map point \( Q(-3, -5) \) to point \( Q'(5, -3) \), we can analyze the coordinates and the nature of the transformations.

1. **Check each transformation option**:

- **A. A 270-degree (counterclockwise) rotation**:
- A 270-degree counterclockwise rotation changes the coordinates \( (x, y) \) to \( (y, -x) \).
- Applying this to \( Q(-3, -5) \):
\[
(-5, 3) \quad \text{(not equal to } Q' (5, -3) \text{)}
\]

- **B. A reflection across the x-axis**:
- Reflecting across the x-axis changes the coordinates \( (x, y) \) to \( (x, -y) \).
- Applying this to \( Q(-3, -5) \):
\[
(-3, 5) \quad \text{(not equal to } Q' (5, -3) \text{)}
\]

- **C. A 90-degree (counterclockwise) rotation**:
- A 90-degree counterclockwise rotation changes the coordinates \( (x, y) \) to \( (-y, x) \).
- Applying this to \( Q(-3, -5) \):
\[
(5, -3) \quad \text{(which matches } Q' (5, -3) \text{)}
\]

- **D. A 180-degree rotation**:
- A 180-degree rotation changes the coordinates \( (x, y) \) to \( (-x, -y) \).
- Applying this to \( Q(-3, -5) \):
\[
(3, 5) \quad \text{(not equal to } Q' (5, -3) \text{)}
\]

After checking each option, the only transformation that correctly maps \( Q(-3, -5) \) to \( Q'(5, -3) \) is **C. a 90-degree (counterclockwise) rotation**.