Question
Which of the following transformations maps ALOW to AL"'O"'W"? Select two correct answers.
(1 point)
the single transformation described by (x, y) → (x, y - 12)
the composite transformation described by rx=1 followed by Tx=7
the single transformation described by (x, y) → (x, y + 12)
the single transformation described by R270°
the composite transformation described by ry=1 followed by ry=7
(1 point)
the single transformation described by (x, y) → (x, y - 12)
the composite transformation described by rx=1 followed by Tx=7
the single transformation described by (x, y) → (x, y + 12)
the single transformation described by R270°
the composite transformation described by ry=1 followed by ry=7
Answers
Answered by
GPT-4o mini
To determine how the transformation maps ALOW to AL"'O"'W", let's analyze the options given.
1. **The single transformation described by \((x, y) → (x, y - 12)\)**: This transformation moves each point down by 12 units. This does not seem to transform ALOW to AL"'O"'W, as this transformation doesn't correspond to the renaming of letters.
2. **The composite transformation described by \(r_x = 1\) followed by \(T_x = 7\)**: It's unclear what \(r_x\) and \(T_x\) mean without further context. However, based on the names, it seems that \(r_x = 1\) might refer to some sort of reflection and \(T_x = 7\) could be a translation. Without specific details, we cannot conclude this is applicable.
3. **The single transformation described by \((x, y) → (x, y + 12)\)**: Similar to option 1, this moves points up by 12 units. Again, this won't work for transforming ALOW to AL"'O"'W.
4. **The single transformation described by \(R_{270°}\)**: This refers to a 270-degree rotation, which changes the orientation of the letters significantly. Depending on their initial orientation, this could correctly account for the transformation into AL"'O"'W.
5. **The composite transformation described by \(r_y = 1\) followed by \(r_y = 7\)**: Again, without context the meanings of these reflections are unclear, but if these were both reflections over the y-axis, they might not correspond to any useful transformation to reach AL"'O"'W.
If I were to choose based on common transformations and assuming some interpretations:
- **A rotation \(R_{270°}\)** could potentially create a transformation to rearrange or reorient the letters.
- For the composite transformation, we don’t have sufficient clarity on the reflection definitions but if they imply a translation and reflection could potentially map letters, it may work.
However, if I had to choose based on a typical interpretation of transformations, I would select options that would likely result in letter modification transformations reflected around the axes:
- **R270°** for angular transformations.
- Depending on reflection and translation meaning having a more positioning or rearrangement effect.
The best way to conclude would be based on visual transformation, but typically the rotation and subsequent movement would form the mapping.
Selecting:
- The option involving \(R_{270°}\).
- And if the reflections had value considering noted translations or rearrangements based on your context of "mapping" letters in a specific direction.
Thus, I would suggest:
- **\(R_{270°}\)**
- Either of the composites if assumed in typical coordinates as mapping contextually would change letter representation (or simply reflecting basis that maps down pattern).
Please check transformations computationally based on their intentions for ideal outputs based on the written movement of letters appearing as transformed uniquely from ALOW.
1. **The single transformation described by \((x, y) → (x, y - 12)\)**: This transformation moves each point down by 12 units. This does not seem to transform ALOW to AL"'O"'W, as this transformation doesn't correspond to the renaming of letters.
2. **The composite transformation described by \(r_x = 1\) followed by \(T_x = 7\)**: It's unclear what \(r_x\) and \(T_x\) mean without further context. However, based on the names, it seems that \(r_x = 1\) might refer to some sort of reflection and \(T_x = 7\) could be a translation. Without specific details, we cannot conclude this is applicable.
3. **The single transformation described by \((x, y) → (x, y + 12)\)**: Similar to option 1, this moves points up by 12 units. Again, this won't work for transforming ALOW to AL"'O"'W.
4. **The single transformation described by \(R_{270°}\)**: This refers to a 270-degree rotation, which changes the orientation of the letters significantly. Depending on their initial orientation, this could correctly account for the transformation into AL"'O"'W.
5. **The composite transformation described by \(r_y = 1\) followed by \(r_y = 7\)**: Again, without context the meanings of these reflections are unclear, but if these were both reflections over the y-axis, they might not correspond to any useful transformation to reach AL"'O"'W.
If I were to choose based on common transformations and assuming some interpretations:
- **A rotation \(R_{270°}\)** could potentially create a transformation to rearrange or reorient the letters.
- For the composite transformation, we don’t have sufficient clarity on the reflection definitions but if they imply a translation and reflection could potentially map letters, it may work.
However, if I had to choose based on a typical interpretation of transformations, I would select options that would likely result in letter modification transformations reflected around the axes:
- **R270°** for angular transformations.
- Depending on reflection and translation meaning having a more positioning or rearrangement effect.
The best way to conclude would be based on visual transformation, but typically the rotation and subsequent movement would form the mapping.
Selecting:
- The option involving \(R_{270°}\).
- And if the reflections had value considering noted translations or rearrangements based on your context of "mapping" letters in a specific direction.
Thus, I would suggest:
- **\(R_{270°}\)**
- Either of the composites if assumed in typical coordinates as mapping contextually would change letter representation (or simply reflecting basis that maps down pattern).
Please check transformations computationally based on their intentions for ideal outputs based on the written movement of letters appearing as transformed uniquely from ALOW.