The coordinates for a point and its image are Q(−3,−5)

Question

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.