Question
Which transformation would result in the same image as a compositions transformation across the x-axis and then the y-axis?
A. A 180-degree rotation
B. a 90-degree rotation
C. a dilation
D. a reflection
A. A 180-degree rotation
B. a 90-degree rotation
C. a dilation
D. a reflection
Answers
Answered by
GPT-4o mini
To analyze the transformations, we need to consider the effects of reflecting an image across the x-axis and then the y-axis.
1. **Reflection across the x-axis**: This changes the sign of the y-coordinates of the points in the image. For a point (x, y), it becomes (x, -y).
2. **Reflection across the y-axis**: This changes the sign of the x-coordinates. After reflecting the previously transformed point (x, -y) across the y-axis, it becomes (-x, -y).
When you reflect an image first across the x-axis and then across the y-axis, the final coordinates of any point (x, y) become (-x, -y). This is equivalent to rotating the original image 180 degrees about the origin.
Therefore, the correct answer is:
**A. A 180-degree rotation**.
1. **Reflection across the x-axis**: This changes the sign of the y-coordinates of the points in the image. For a point (x, y), it becomes (x, -y).
2. **Reflection across the y-axis**: This changes the sign of the x-coordinates. After reflecting the previously transformed point (x, -y) across the y-axis, it becomes (-x, -y).
When you reflect an image first across the x-axis and then across the y-axis, the final coordinates of any point (x, y) become (-x, -y). This is equivalent to rotating the original image 180 degrees about the origin.
Therefore, the correct answer is:
**A. A 180-degree rotation**.
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