Question
The triangles are congruent by the SSS congruence theorem.
Triangles L M N and L prime M prime N prime are shown. Triangle L M N is rotated about point L and then is shifted up and to the right to form triangle L prime M prime N prime.
Which transformation(s) can map ΔLMN onto ΔL'M'N'?
translation only
reflection only
rotation then translation
reflection then translation
Triangles L M N and L prime M prime N prime are shown. Triangle L M N is rotated about point L and then is shifted up and to the right to form triangle L prime M prime N prime.
Which transformation(s) can map ΔLMN onto ΔL'M'N'?
translation only
reflection only
rotation then translation
reflection then translation
Answers
Answered by
GPT-4o mini
To determine which transformation(s) can map triangle ΔLMN onto triangle ΔL'M'N', we analyze the transformations involved as described in your question.
1. **Rotation**: You mentioned that triangle ΔLMN is rotated about point L. This indicates that the vertices of the triangle are repositioned while maintaining their respective distances to point L. This would maintain congruence since rotation preserves distance and angle measures.
2. **Translation**: After the rotation, triangle ΔLMN is shifted up and to the right, which is a translation. Translation also preserves distances and angles.
Given these two transformations—rotation followed by translation—are what are used to map triangle ΔLMN onto triangle ΔL'M'N', the correct choice would be:
**rotation then translation**
So, among your options, the one that accurately represents the transformations used is:
- **rotation then translation**
1. **Rotation**: You mentioned that triangle ΔLMN is rotated about point L. This indicates that the vertices of the triangle are repositioned while maintaining their respective distances to point L. This would maintain congruence since rotation preserves distance and angle measures.
2. **Translation**: After the rotation, triangle ΔLMN is shifted up and to the right, which is a translation. Translation also preserves distances and angles.
Given these two transformations—rotation followed by translation—are what are used to map triangle ΔLMN onto triangle ΔL'M'N', the correct choice would be:
**rotation then translation**
So, among your options, the one that accurately represents the transformations used is:
- **rotation then translation**