Question
What composition transformation occurs in the following? (x,y)→(y+5,−x)
(1 point)
Responses
a reflection across the y-axis and a translation down by 5
a reflection across the y -axis and a translation down by 5
a 90-degree clockwise rotation and a translation to the right by 5
a 90-degree clockwise rotation and a translation to the right by 5
a 90-degree counterclockwise rotation and a translation down by 5
a 90-degree counterclockwise rotation and a translation down by 5
a reflection across the x-axis and a translation 5 right
(1 point)
Responses
a reflection across the y-axis and a translation down by 5
a reflection across the y -axis and a translation down by 5
a 90-degree clockwise rotation and a translation to the right by 5
a 90-degree clockwise rotation and a translation to the right by 5
a 90-degree counterclockwise rotation and a translation down by 5
a 90-degree counterclockwise rotation and a translation down by 5
a reflection across the x-axis and a translation 5 right
Answers
GPT-4o mini
To determine the composition transformation for the mapping \((x,y) → (y+5,−x)\), we will analyze the transformations step-by-step.
1. The transformation takes the first coordinate \(x\) and maps it to \(-x\). This indicates a reflection across the y-axis.
2. The second coordinate \(y\) is mapped to \(y + 5\), which indicates a translation upward by 5 units.
Thus, the total transformation consists of the following:
- A reflection across the y-axis (due to the \(-x\) component).
- A translation upwards by 5 (due to the \(y + 5\) component).
Among the provided options, the one closest to our analysis is:
- **a reflection across the y-axis and a translation up by 5**.
However, this specific choice isn't present in your options. The correct option, based solely on the transformations listed, is:
**a reflection across the x-axis and a translation 5 right**
(The provided options may not have a matching response according to the transformations derived). Please verify the provided options.
1. The transformation takes the first coordinate \(x\) and maps it to \(-x\). This indicates a reflection across the y-axis.
2. The second coordinate \(y\) is mapped to \(y + 5\), which indicates a translation upward by 5 units.
Thus, the total transformation consists of the following:
- A reflection across the y-axis (due to the \(-x\) component).
- A translation upwards by 5 (due to the \(y + 5\) component).
Among the provided options, the one closest to our analysis is:
- **a reflection across the y-axis and a translation up by 5**.
However, this specific choice isn't present in your options. The correct option, based solely on the transformations listed, is:
**a reflection across the x-axis and a translation 5 right**
(The provided options may not have a matching response according to the transformations derived). Please verify the provided options.