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

a −90
-degree (clockwise) rotation
a negative 90 -degree (clockwise) rotation

a 270-degree (counterclockwise) rotation

Answer 1

To determine which transformation occurred from point \( Q(-3, -5) \) to point \( Q'(5, -3) \), we can analyze the coordinates.

1. First, let's calculate the changes in the coordinates:
- Original point: \( Q(-3, -5) \)
- Transformed point: \( Q'(5, -3) \)

2. To visualize the transformation, let's analyze the individual transformations:

- **90-degree (counterclockwise) rotation**:
The rule is \( (x, y) \rightarrow (-y, x) \)
- Applying to \( Q(-3, -5) \):
- New coordinates: \( (5, -3) \) (this matches \( Q' \))

- **90-degree (clockwise) rotation**:
The rule is \( (x, y) \rightarrow (y, -x) \)
- Applying to \( Q(-3, -5) \):
- New coordinates: \( (-5, 3) \) (not a match)

- **180-degree rotation (clockwise or counterclockwise)**:
The rule for both is \( (x, y) \rightarrow (-x, -y) \)
- Applying to \( Q(-3, -5) \):
- New coordinates: \( (3, 5) \) (not a match)

- **270-degree (counterclockwise) rotation** (which is the same as a 90-degree clockwise):
The rule is equivalent and gives the same output as the 90-degree clockwise rotation, so it would also yield \( (-5, 3) \) (not a match).

Given that a \( 90 \)-degree counterclockwise rotation from point \( Q(-3, -5) \) properly leads to point \( Q'(5, -3) \), the transformation that occurred is:

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