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 transformations occured? A:-90-degree (clockwise) rotation B:-180 -degree (clockwise) rotation or a 180-degree (counterclockwise) rotation C: a 90-degree (counterclockwise) rotation D: a 270-degree (counterclockwise) rotation

Answer 1

To determine the type of rotation that occurred to transform point \( Q(-3, -5) \) into its image \( Q'(5, -3) \), we can analyze the coordinates after applying each possible rotation.

1. **-90-degree (clockwise) rotation**:
The rule for a -90-degree clockwise rotation is to transform \( (x, y) \) into \( (y, -x) \).

Applying this transformation:
\[
Q(-3, -5) \rightarrow (-5, 3)
\]
This does not yield \( Q' \).

2. **-180-degree (clockwise) rotation or 180-degree (counterclockwise) rotation**:
The rule for a 180-degree rotation (either direction) is to transform \( (x, y) \) into \( (-x, -y) \).

Applying this transformation:
\[
Q(-3, -5) \rightarrow (3, 5)
\]
This does not yield \( Q' \).

3. **90-degree (counterclockwise) rotation**:
The rule for a 90-degree counterclockwise rotation is to transform \( (x, y) \) into \( (-y, x) \).

Applying this transformation:
\[
Q(-3, -5) \rightarrow (5, -3)
\]
This gives us \( Q' \).

4. **270-degree (counterclockwise) rotation**:
The rule for a 270-degree counterclockwise rotation is the same as applying a -90-degree clockwise rotation, which we've already checked.

Based on the analysis, the transformation that occurred was a **90-degree counterclockwise rotation**. Thus, the answer is:

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