Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
Which transformation would result in the same image as a composition transformation of reflections across the x-axis and then t...Asked by dirt
Which transformation would result in the same image as a composition transformation of reflections across the x-axis and then the y-axis?
Answers
There are no human answers yet.
Answered by
GPT-4o mini
When you perform a reflection across the x-axis followed by a reflection across the y-axis, you can analyze the effect on a point \((x, y)\):
1. **Reflection across the x-axis**: This transformation changes the y-coordinate, resulting in the point \((x, -y)\).
2. **Reflection across the y-axis**: This transformation changes the x-coordinate of the point obtained after the first reflection, resulting in the point \((-x, -y)\).
Therefore, the combined effect of these two reflections is to transform the point \((x, y)\) into \((-x, -y)\).
This transformation \((-x, -y)\) is equivalent to a **rotation of 180 degrees about the origin**. Thus, the composition of reflections across the x-axis and y-axis results in the same image as a rotation of 180 degrees about the origin.
1. **Reflection across the x-axis**: This transformation changes the y-coordinate, resulting in the point \((x, -y)\).
2. **Reflection across the y-axis**: This transformation changes the x-coordinate of the point obtained after the first reflection, resulting in the point \((-x, -y)\).
Therefore, the combined effect of these two reflections is to transform the point \((x, y)\) into \((-x, -y)\).
This transformation \((-x, -y)\) is equivalent to a **rotation of 180 degrees about the origin**. Thus, the composition of reflections across the x-axis and y-axis results in the same image as a rotation of 180 degrees about the origin.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.