Question
Use the image to determine the direction and angle of rotation.
graph of triangle ABC in quadrant 4 and a second polygon A prime B prime C prime in quadrant 3
90° clockwise rotation
90° counterclockwise rotation
180° clockwise rotation
360° counterclockwise rotation
graph of triangle ABC in quadrant 4 and a second polygon A prime B prime C prime in quadrant 3
90° clockwise rotation
90° counterclockwise rotation
180° clockwise rotation
360° counterclockwise rotation
Answers
Answered by
GPT-4o mini
To determine the direction and angle of rotation from triangle ABC in quadrant IV to triangle A'B'C' in quadrant III, we can analyze the change in coordinates for the points.
1. A 90° clockwise rotation would move points from quadrant IV (with negative y-coordinate and positive x-coordinate) to quadrant I (with positive x and y coordinates), which is not the case here.
2. A 90° counterclockwise rotation would move points from quadrant IV to quadrant II, which is also not applicable.
3. A 180° rotation, however, would take points in quadrant IV and move them to quadrant II (if we consider the effect of flipping over both axes), matching the notion of both triangles being mirrors of each other varying by 180°.
4. A 360° counterclockwise rotation would leave the triangle unchanged, which does not apply if we are transitioning from one triangle to another.
Given that triangle A'B'C' is in quadrant III, while triangle ABC is in quadrant IV, the most fitting description of the rotation from ABC to A'B'C' is **180° clockwise rotation**.
Thus, the correct answer is:
**180° clockwise rotation.**
1. A 90° clockwise rotation would move points from quadrant IV (with negative y-coordinate and positive x-coordinate) to quadrant I (with positive x and y coordinates), which is not the case here.
2. A 90° counterclockwise rotation would move points from quadrant IV to quadrant II, which is also not applicable.
3. A 180° rotation, however, would take points in quadrant IV and move them to quadrant II (if we consider the effect of flipping over both axes), matching the notion of both triangles being mirrors of each other varying by 180°.
4. A 360° counterclockwise rotation would leave the triangle unchanged, which does not apply if we are transitioning from one triangle to another.
Given that triangle A'B'C' is in quadrant III, while triangle ABC is in quadrant IV, the most fitting description of the rotation from ABC to A'B'C' is **180° clockwise rotation**.
Thus, the correct answer is:
**180° clockwise rotation.**