Question
Ben transformed a figure from quadrant IV to quadrant I. The pre-image and image are congruent figures, but the orientation of the figure changed. Which could be the transformation Ben used?
A reflection over the y-axis
A translation up
A rotation 90° counterclockwise
A dilation by a scale factor of 2
A reflection over the y-axis
A translation up
A rotation 90° counterclockwise
A dilation by a scale factor of 2
Answers
GPT-4o mini
To determine the transformation Ben used to move a figure from quadrant IV to quadrant I while changing its orientation, we should analyze each option:
1. **A reflection over the y-axis**: This would keep the figure in the same relative position but would mirror it across the y-axis, taking points from quadrant IV to quadrant III, not quadrant I.
2. **A translation up**: This would move the figure vertically, keeping it congruent but would not change its orientation. Thus, it would remain in quadrant IV, just shifted up, and not reach quadrant I.
3. **A rotation 90° counterclockwise**: If a figure in quadrant IV is rotated 90° counterclockwise, it will move to quadrant I. This transformation also changes the orientation of the figure.
4. **A dilation by a scale factor of 2**: A dilation scales the figure larger or smaller but does not change its position relative to the origin or its orientation, so it wouldn't result in a move from quadrant IV to quadrant I.
Given these analyses, the correct answer is:
**A rotation 90° counterclockwise.**
1. **A reflection over the y-axis**: This would keep the figure in the same relative position but would mirror it across the y-axis, taking points from quadrant IV to quadrant III, not quadrant I.
2. **A translation up**: This would move the figure vertically, keeping it congruent but would not change its orientation. Thus, it would remain in quadrant IV, just shifted up, and not reach quadrant I.
3. **A rotation 90° counterclockwise**: If a figure in quadrant IV is rotated 90° counterclockwise, it will move to quadrant I. This transformation also changes the orientation of the figure.
4. **A dilation by a scale factor of 2**: A dilation scales the figure larger or smaller but does not change its position relative to the origin or its orientation, so it wouldn't result in a move from quadrant IV to quadrant I.
Given these analyses, the correct answer is:
**A rotation 90° counterclockwise.**