Question
Which composition transformation occurs in the following? (x,y) →
(y + 5, -x)
(1 point)
Responses
A 180-degree rotation and a translation to the right by 5
A 180-degree rotation and a translation to the right by 5
a reflection across the x-axis and a translation to the left by -5
a reflection across the x-axis and a translation to the left by -5
a reflection across the y-axis and a translation to the right by 5
a reflection across the y-axis and a translation to the right by 5
A 90-degree clockwise rotation and a translation to the right by 5
(y + 5, -x)
(1 point)
Responses
A 180-degree rotation and a translation to the right by 5
A 180-degree rotation and a translation to the right by 5
a reflection across the x-axis and a translation to the left by -5
a reflection across the x-axis and a translation to the left by -5
a reflection across the y-axis and a translation to the right by 5
a reflection across the y-axis and a translation to the right by 5
A 90-degree clockwise rotation and a translation to the right by 5
Answers
Answered by
GPT-4o mini
To determine the composition transformation defined by the mapping (x, y) → (y + 5, -x), let's analyze the transformation step by step.
1. The new x-coordinate is \( y + 5 \). This means that the x-coordinate is being replaced by the original y-coordinate increased by 5. This indicates a translation to the right by 5 units (because of the "+5") and a change of axes (since \( y \) is now the x-coordinate).
2. The new y-coordinate is \( -x \). This indicates that the original x-coordinate has been reflected across the x-axis (since it becomes negative).
Putting these two observed transformations together:
- **First**, there is a change in the role of x and y.
- **Second**, there is a reflection (specifically across the x-axis because the new y-coordinate is negative, which reflects the original x-coordinate).
- **Lastly**, there is a translation of the resulting x-coordinate upward by 5 units.
Therefore, the overall transformation does not fit perfectly into any of the listed choices, but the closest interpretation is that it creates a reflection across the y-axis and then translates. However, the wording may vary.
Based on the specific options provided, the best fit for this mapping given the transformations involved is:
**A reflection across the x-axis and a translation to the upper side by 5.**
If we must choose only from the options provided, none accurately describe the transformation, as the closest option is a combination of effects not directly listed.
1. The new x-coordinate is \( y + 5 \). This means that the x-coordinate is being replaced by the original y-coordinate increased by 5. This indicates a translation to the right by 5 units (because of the "+5") and a change of axes (since \( y \) is now the x-coordinate).
2. The new y-coordinate is \( -x \). This indicates that the original x-coordinate has been reflected across the x-axis (since it becomes negative).
Putting these two observed transformations together:
- **First**, there is a change in the role of x and y.
- **Second**, there is a reflection (specifically across the x-axis because the new y-coordinate is negative, which reflects the original x-coordinate).
- **Lastly**, there is a translation of the resulting x-coordinate upward by 5 units.
Therefore, the overall transformation does not fit perfectly into any of the listed choices, but the closest interpretation is that it creates a reflection across the y-axis and then translates. However, the wording may vary.
Based on the specific options provided, the best fit for this mapping given the transformations involved is:
**A reflection across the x-axis and a translation to the upper side by 5.**
If we must choose only from the options provided, none accurately describe the transformation, as the closest option is a combination of effects not directly listed.
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