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 below.
Reflection across the x-axis
180° counterclockwise rotation
Horizontal translation
Vertical translation
Image of polygon ABCD and a second polygon A prime B prime C prime D prime below.
Reflection across the x-axis
180° counterclockwise rotation
Horizontal translation
Vertical translation
Answers
Answered by
GPT-4o mini
To determine the type of transformation shown between polygon ABCD and polygon A'B'C'D', you need to consider the positioning of the two polygons relative to each other.
1. **Reflection across the x-axis**: If A'B'C'D' is the mirror image of ABCD across the x-axis, each point would have the same x-coordinate and the y-coordinates would change sign (e.g., (x, y) becomes (x, -y)).
2. **180° counterclockwise rotation**: This transformation means that each point of the original polygon would move to a position that is directly opposite around the center point (rotate 180°). For instance, a point (x, y) would change to (-x, -y).
3. **Horizontal translation**: In this case, every point would move the same distance left or right, meaning the x-coordinates would change while the y-coordinates stay the same.
4. **Vertical translation**: Here, every point would move the same distance up or down, meaning the y-coordinates would change while the x-coordinates remain the same.
Without the actual image, you would need to visualize or apply these points based on the positioning of the polygons. If you can identify the coordinates of points before and after the transformation, you can confirm if it's one of these transformations.
- Check if the y-coordinates of each point of A'B'C'D' are the opposite of A, B, C, D to confirm reflection.
- Check if they are quadrants apart to confirm 180° rotation.
- Check if points all have the same y-coordinate for horizontal translation or the same x-coordinate for vertical translation.
Once you analyze the above characteristics, you should be able to identify the specific transformation.
1. **Reflection across the x-axis**: If A'B'C'D' is the mirror image of ABCD across the x-axis, each point would have the same x-coordinate and the y-coordinates would change sign (e.g., (x, y) becomes (x, -y)).
2. **180° counterclockwise rotation**: This transformation means that each point of the original polygon would move to a position that is directly opposite around the center point (rotate 180°). For instance, a point (x, y) would change to (-x, -y).
3. **Horizontal translation**: In this case, every point would move the same distance left or right, meaning the x-coordinates would change while the y-coordinates stay the same.
4. **Vertical translation**: Here, every point would move the same distance up or down, meaning the y-coordinates would change while the x-coordinates remain the same.
Without the actual image, you would need to visualize or apply these points based on the positioning of the polygons. If you can identify the coordinates of points before and after the transformation, you can confirm if it's one of these transformations.
- Check if the y-coordinates of each point of A'B'C'D' are the opposite of A, B, C, D to confirm reflection.
- Check if they are quadrants apart to confirm 180° rotation.
- Check if points all have the same y-coordinate for horizontal translation or the same x-coordinate for vertical translation.
Once you analyze the above characteristics, you should be able to identify the specific transformation.