Question
Which of the following transformations maps △LOW to △L''O''W''? Select two correct answers.
(1 point)
Responses
the composite transformation described by rx=1 followed by rx=7the composite transformation described by r sub x is equal to 1 followed by r sub x is equal to 7
the single transformation described by (x,y)→(x,y−12)
the single transformation described by open paren x comma y close paren rightarrow open paren x comma y minus 12 close paren
the composite transformation described by ry=1 followed by ry=7the composite transformation described by r sub y is equal to 1 followed by r sub y is equal to 7
the single transformation described by (x,y)→(x,y+12)
the single transformation described by open paren x comma y close paren rightarrow open paren x comma y plus 12 close paren
the single transformation described by R270°
(1 point)
Responses
the composite transformation described by rx=1 followed by rx=7the composite transformation described by r sub x is equal to 1 followed by r sub x is equal to 7
the single transformation described by (x,y)→(x,y−12)
the single transformation described by open paren x comma y close paren rightarrow open paren x comma y minus 12 close paren
the composite transformation described by ry=1 followed by ry=7the composite transformation described by r sub y is equal to 1 followed by r sub y is equal to 7
the single transformation described by (x,y)→(x,y+12)
the single transformation described by open paren x comma y close paren rightarrow open paren x comma y plus 12 close paren
the single transformation described by R270°
Answers
Answered by
GPT-4o mini
To determine which transformations map \( \triangle LOW \) to \( \triangle L''O''W'' \), we need to analyze the options provided and identify the transformations.
1. **Composite transformation described by \( r_x = 1 \) followed by \( r_x = 7 \)**: This transformation refers to reflections across horizontal lines at \( y = 1 \) and \( y = 7 \). Without specific coordinates or angles, it is hard to assess its appropriateness.
2. **Single transformation described by \( (x,y) \rightarrow (x,y-12) \)**: This transformation translates every point downwards by 12 units. If \( \triangle LOW \) gets translated downwards, this could be a valid transformation.
3. **Composite transformation described by \( r_y = 1 \) followed by \( r_y = 7 \)**: Similar to the first option but this time applies to vertical reflections across \( x = 1 \) and \( x = 7 \). As in the previous reflections, we would require specific transformations or information about \( \triangle LOW \) positions.
4. **Single transformation described by \( (x,y) \rightarrow (x,y+12) \)**: This transformation translates every point upwards by 12 units. If \( \triangle LOW \) were located below \( \triangle L''O''W'' \), this could also be valid, but, without information about their relative positions, we can’t confirm this.
5. **Single transformation described by \( R_{270^\circ} \)**: A rotation of 270 degrees counter-clockwise would reposition the triangle in a specific way based on where the vertices of \( \triangle LOW \) are located. This could also be valid depending on orientation.
### Conclusion
Without specific information about the location and positions of vertices in \( \triangle LOW \) and \( \triangle L''O''W'' \), we cannot definitively pick two transformations. However, common practices indicate looking for movement that places \( \triangle LOW \) into an expected vertical or horizontal alignment with \( \triangle L''O''W'' \).
From the translations provided:
- **The single transformation \( (x,y) \rightarrow (x,y - 12) \)** would be appropriate if \( \triangle L''O''W'' \) is directly below \( \triangle LOW \).
- **The single transformation \( (x,y) \rightarrow (x,y + 12) \)** would be appropriate if \( \triangle L''O''W'' \) is directly above \( \triangle LOW \).
Thus, it’s reasonable to choose the translations:
- **The single transformation \( (x,y) \rightarrow (x,y - 12) \)**
- **The single transformation \( (x,y) \rightarrow (x,y + 12) \)**
Both translations are plausible depending on the relative positions of the triangles. However, if given they are exact transformations mapping one directly to another, without loss of information, the translation that moves down is a likely candidate.
Please clarify the specific coordinates or visual representation for precise information.
1. **Composite transformation described by \( r_x = 1 \) followed by \( r_x = 7 \)**: This transformation refers to reflections across horizontal lines at \( y = 1 \) and \( y = 7 \). Without specific coordinates or angles, it is hard to assess its appropriateness.
2. **Single transformation described by \( (x,y) \rightarrow (x,y-12) \)**: This transformation translates every point downwards by 12 units. If \( \triangle LOW \) gets translated downwards, this could be a valid transformation.
3. **Composite transformation described by \( r_y = 1 \) followed by \( r_y = 7 \)**: Similar to the first option but this time applies to vertical reflections across \( x = 1 \) and \( x = 7 \). As in the previous reflections, we would require specific transformations or information about \( \triangle LOW \) positions.
4. **Single transformation described by \( (x,y) \rightarrow (x,y+12) \)**: This transformation translates every point upwards by 12 units. If \( \triangle LOW \) were located below \( \triangle L''O''W'' \), this could also be valid, but, without information about their relative positions, we can’t confirm this.
5. **Single transformation described by \( R_{270^\circ} \)**: A rotation of 270 degrees counter-clockwise would reposition the triangle in a specific way based on where the vertices of \( \triangle LOW \) are located. This could also be valid depending on orientation.
### Conclusion
Without specific information about the location and positions of vertices in \( \triangle LOW \) and \( \triangle L''O''W'' \), we cannot definitively pick two transformations. However, common practices indicate looking for movement that places \( \triangle LOW \) into an expected vertical or horizontal alignment with \( \triangle L''O''W'' \).
From the translations provided:
- **The single transformation \( (x,y) \rightarrow (x,y - 12) \)** would be appropriate if \( \triangle L''O''W'' \) is directly below \( \triangle LOW \).
- **The single transformation \( (x,y) \rightarrow (x,y + 12) \)** would be appropriate if \( \triangle L''O''W'' \) is directly above \( \triangle LOW \).
Thus, it’s reasonable to choose the translations:
- **The single transformation \( (x,y) \rightarrow (x,y - 12) \)**
- **The single transformation \( (x,y) \rightarrow (x,y + 12) \)**
Both translations are plausible depending on the relative positions of the triangles. However, if given they are exact transformations mapping one directly to another, without loss of information, the translation that moves down is a likely candidate.
Please clarify the specific coordinates or visual representation for precise information.