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.
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Identify the vertices of the triangles:
- Triangle \( \triangle PBK \): Points P, B, K
- Triangle \( \triangle LQA \): Points L, Q, A
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Consider the matching of the vertices:
- We want to find a transformation that aligns the points in the triangles correctly.
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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."
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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.