Question
Use the image to determine the direction and angle of rotation.
Graph of polygon ABCD in quadrant 2 with point A at negative 6 comma 5. A second polygon A prime B prime C prime D prime in quadrant 4 with point A prime at 6 comma negative 5.
90° clockwise rotation
90° counterclockwise rotation
180° counterclockwise rotation
270° clockwise rotation
Graph of polygon ABCD in quadrant 2 with point A at negative 6 comma 5. A second polygon A prime B prime C prime D prime in quadrant 4 with point A prime at 6 comma negative 5.
90° clockwise rotation
90° counterclockwise rotation
180° counterclockwise rotation
270° clockwise rotation
Answers
Answered by
GPT-4o mini
To determine the direction and angle of rotation from polygon ABCD to polygon A'B'C'D', let's look at the coordinates provided for points A and A':
- Point A is at (-6, 5) in quadrant 2.
- Point A' is at (6, -5) in quadrant 4.
To analyze the rotation:
1. Identify the transformation from point A to point A':
- The x-coordinate changes from -6 to 6, which is a change of +12.
- The y-coordinate changes from 5 to -5, which is a change of -10.
2. The general rule for a 90° clockwise rotation about the origin transforms a point (x, y) to (y, -x). Let's check if that applies:
- For A(-6, 5):
If we apply a 90° clockwise rotation:
- The new coordinates would be (5, 6) which does not match A'.
3. Now let's check for a 90° counterclockwise rotation. The transformation for this rotation is (x, y) to (-y, x):
- Applying this to A(-6, 5):
- New coordinates would be (-5, -6) which also does not match A'.
4. Next, consider a 180° rotation. The transformation takes (x, y) to (-x, -y):
- Applying this to A(-6, 5):
- New coordinates would be (6, -5), which indeed matches A'.
Thus, the direction and angle of rotation from polygon ABCD to polygon A'B'C'D' is:
**180° counterclockwise rotation.**
- Point A is at (-6, 5) in quadrant 2.
- Point A' is at (6, -5) in quadrant 4.
To analyze the rotation:
1. Identify the transformation from point A to point A':
- The x-coordinate changes from -6 to 6, which is a change of +12.
- The y-coordinate changes from 5 to -5, which is a change of -10.
2. The general rule for a 90° clockwise rotation about the origin transforms a point (x, y) to (y, -x). Let's check if that applies:
- For A(-6, 5):
If we apply a 90° clockwise rotation:
- The new coordinates would be (5, 6) which does not match A'.
3. Now let's check for a 90° counterclockwise rotation. The transformation for this rotation is (x, y) to (-y, x):
- Applying this to A(-6, 5):
- New coordinates would be (-5, -6) which also does not match A'.
4. Next, consider a 180° rotation. The transformation takes (x, y) to (-x, -y):
- Applying this to A(-6, 5):
- New coordinates would be (6, -5), which indeed matches A'.
Thus, the direction and angle of rotation from polygon ABCD to polygon A'B'C'D' is:
**180° counterclockwise rotation.**