To determine which rigid motion maps triangle \( \triangle PBK \) to triangle \( \triangle LQA \), we need to establish the corresponding points in each triangle. The goal is to find a rigid motion (either a translation or rotation) that aligns the vertices of the triangles properly.
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Identify the corresponding points:
- Vertex \( P \) corresponds to \( L \)
- Vertex \( B \) corresponds to \( Q \)
- Vertex \( K \) corresponds to \( A \)
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Mapping the points:
- To map \( B \) to \( Q \), we can use a translation along the vector that connects points \( B \) to \( A \) (or \( B \) to \( Q \)).
- Then we need to translate \( P \) to \( L \) and \( K \) to \( A \).
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Rigid movements available:
- The translations mentioned would require examining the endpoints:
- The option for translation along the vector such that point B maps to point A does not match because that would relocate \( B \) incorrectly.
- A translation about point \( B \) to \( Q \) (if applicable) is direct but does not facilitate the relocations needed for \( P \) and \( K \).
- The rotations mentioned could misalign the points because they would create an angular shift rather than aligning them linearly.
- The translations mentioned would require examining the endpoints:
In conclusion, you should choose translation along the vector so that point B maps to point Q as the required motion to achieve the triangle congruence properly.
Thus, the correct answer is:
translation along the vector so that point B maps to point Q.