Question
Use the image to determine the type of transformation shown.
Image of polygon ABCD and a second polygon A prime B prime C prime D prime to the left.
Reflection across the y-axis
270° counterclockwise rotation
Vertical translation
Horizontal translation
Image of polygon ABCD and a second polygon A prime B prime C prime D prime to the left.
Reflection across the y-axis
270° counterclockwise rotation
Vertical translation
Horizontal translation
Answers
Answered by
GPT-4o mini
To determine the type of transformation shown between polygon ABCD and polygon A'B'C'D', you should analyze the position and orientation of the polygons.
1. **Reflection across the y-axis**: This would mean that the new polygon A'B'C'D' would be a mirror image of polygon ABCD on the opposite side of the y-axis.
2. **270° counterclockwise rotation**: This would rotate the polygon around a point (usually the origin) in a counterclockwise direction by 270 degrees.
3. **Vertical translation**: This would move the polygon up or down along the y-axis without changing its orientation or shape.
4. **Horizontal translation**: This would move the polygon left or right along the x-axis without changing its orientation or shape.
To accurately determine which transformation has taken place, consider how the points of ABCD differ from those of A'B'C'D'. If the shapes are oriented the same but shifted, it could be a translation. If one shape is flipped compared to the other, it's a reflection. If it appears to have rotated, it's either a rotation (could be 90, 180, 270 degrees).
Based on the description of the polygons and their arrangement, the answer will be one of the transformations listed. If A'B'C'D' appears laterally inverted compared to ABCD with the same height and width, then it's a reflection across the y-axis. If it appears to have shifted without flipping or rotating, then it might be a translation.
Please examine the image with these definitions in mind to determine the correct transformation type.
1. **Reflection across the y-axis**: This would mean that the new polygon A'B'C'D' would be a mirror image of polygon ABCD on the opposite side of the y-axis.
2. **270° counterclockwise rotation**: This would rotate the polygon around a point (usually the origin) in a counterclockwise direction by 270 degrees.
3. **Vertical translation**: This would move the polygon up or down along the y-axis without changing its orientation or shape.
4. **Horizontal translation**: This would move the polygon left or right along the x-axis without changing its orientation or shape.
To accurately determine which transformation has taken place, consider how the points of ABCD differ from those of A'B'C'D'. If the shapes are oriented the same but shifted, it could be a translation. If one shape is flipped compared to the other, it's a reflection. If it appears to have rotated, it's either a rotation (could be 90, 180, 270 degrees).
Based on the description of the polygons and their arrangement, the answer will be one of the transformations listed. If A'B'C'D' appears laterally inverted compared to ABCD with the same height and width, then it's a reflection across the y-axis. If it appears to have shifted without flipping or rotating, then it might be a translation.
Please examine the image with these definitions in mind to determine the correct transformation type.