Question
What composition transformation occurs in the following? (x,y) arrow (y+5, -x)
A: a reflection across the y-axis and a translation down by 5
B: a 90-degree clockwise rotation and a translation to the right by 5
C: a 90-degree counterclockwise rotation and a translation down by 5
A: a reflection across the y-axis and a translation down by 5
B: a 90-degree clockwise rotation and a translation to the right by 5
C: a 90-degree counterclockwise rotation and a translation down by 5
Answers
GPT-4o mini
To analyze the transformation from \((x, y)\) to \((y + 5, -x)\), let's break it down step by step.
1. **Identify the first part of the transformation**:
- The new \(x\)-coordinate is \(y + 5\).
- This indicates a transformation that involves both changing the \(y\) value and translating it vertically upward by 5 units because we have \(y + 5\).
2. **Identify the second part of the transformation**:
- The new \(y\)-coordinate is \(-x\).
- This represents a reflection across the \(y\)-axis, as the \(x\) coordinate is negated to obtain the new \(y\) coordinate.
Now, let's evaluate the choices:
- Choice A: a reflection across the y-axis and a translation down by 5.
- While the reflection part is correct, the translation is upward, not down.
- Choice B: a 90-degree clockwise rotation and a translation to the right by 5.
- This description does not match, as a rotation wouldn't yield \(y + 5\) as the new \(x\)-coordinate.
- Choice C: a 90-degree counterclockwise rotation and a translation down by 5.
- This also does not match, as there is no rotation involved that would lead to this transformation.
We conclude that the answer is not present in these options. The transformation consists of a reflection across the \(y\)-axis and a translation upwards by \(5\).
1. **Identify the first part of the transformation**:
- The new \(x\)-coordinate is \(y + 5\).
- This indicates a transformation that involves both changing the \(y\) value and translating it vertically upward by 5 units because we have \(y + 5\).
2. **Identify the second part of the transformation**:
- The new \(y\)-coordinate is \(-x\).
- This represents a reflection across the \(y\)-axis, as the \(x\) coordinate is negated to obtain the new \(y\) coordinate.
Now, let's evaluate the choices:
- Choice A: a reflection across the y-axis and a translation down by 5.
- While the reflection part is correct, the translation is upward, not down.
- Choice B: a 90-degree clockwise rotation and a translation to the right by 5.
- This description does not match, as a rotation wouldn't yield \(y + 5\) as the new \(x\)-coordinate.
- Choice C: a 90-degree counterclockwise rotation and a translation down by 5.
- This also does not match, as there is no rotation involved that would lead to this transformation.
We conclude that the answer is not present in these options. The transformation consists of a reflection across the \(y\)-axis and a translation upwards by \(5\).