Question
To prove the triangles are congruent, which of the following rigid motions would map △PBK to △LQA? (1 point) Responses translation along the vector so that point B maps to point A translation along the vector so that point upper B maps to point upper A rotation of 180° (counterclockwise) about point B rotation of 180 degrees (counterclockwise) about point upper B translation along the vector so that point P maps to point A translation along the vector so that point upper P maps to point upper A translation along the vector so that point B maps to point Q
Answers
GPT-4o mini
To determine which rigid motion would map triangle \( \triangle PBK \) to triangle \( \triangle LQA \), we need to analyze the points and find a corresponding transformation.
1. Identify the vertices of the triangles:
- Triangle \( \triangle PBK \): Points P, B, K
- Triangle \( \triangle LQA \): Points L, Q, A
2. Consider the matching of the vertices:
- We want to find a transformation that aligns the points in the triangles correctly.
3. Analyzing the options:
- **Translation along the vector so that point B maps to point A**: This would move point B to A, but we need to check if it aligns the other points.
- **Translation along the vector so that point B maps to point Q**: This could potentially work if it aligns the other corresponding points after moving B to Q.
- **Rotation of 180° about point B**: This would not map point B to point A nor either P or K to L or Q or A consistently.
- **Translation along the vector so that point P maps to point A**: This would move P to A, but we need to see if it relates B and K to the corresponding points.
- **Translation along the vector so that point P maps to point upper A**: This appears similar but is not clearly defined without knowing which point is "upper."
4. Selecting a conclusion logically:
To complete the mapping, the translation that specifically matches the vertices is crucial. The most relevant motion appears to be **translation along the vector so that point B maps to point Q**, as it directly relates B and Q corresponding to the triangles.
Thus, the best option is:
**Translation along the vector so that point B maps to point Q.**
1. Identify the vertices of the triangles:
- Triangle \( \triangle PBK \): Points P, B, K
- Triangle \( \triangle LQA \): Points L, Q, A
2. Consider the matching of the vertices:
- We want to find a transformation that aligns the points in the triangles correctly.
3. Analyzing the options:
- **Translation along the vector so that point B maps to point A**: This would move point B to A, but we need to check if it aligns the other points.
- **Translation along the vector so that point B maps to point Q**: This could potentially work if it aligns the other corresponding points after moving B to Q.
- **Rotation of 180° about point B**: This would not map point B to point A nor either P or K to L or Q or A consistently.
- **Translation along the vector so that point P maps to point A**: This would move P to A, but we need to see if it relates B and K to the corresponding points.
- **Translation along the vector so that point P maps to point upper A**: This appears similar but is not clearly defined without knowing which point is "upper."
4. Selecting a conclusion logically:
To complete the mapping, the translation that specifically matches the vertices is crucial. The most relevant motion appears to be **translation along the vector so that point B maps to point Q**, as it directly relates B and Q corresponding to the triangles.
Thus, the best option is:
**Translation along the vector so that point B maps to point Q.**