To determine which rigid motion would map triangle \( \triangle PBK \) to triangle \( \triangle LQA \), we need to analyze the points involved and check if any of the offered translations or rotations can successfully accomplish this mapping.
- Translations can only move points straight along a line, and they will not change the orientation or relative positions of the points involved.
- Rotations can change the orientation of the points, but we need to ensure the angles and sides correspond correctly.
To map \( \triangle PBK \) to \( \triangle LQA \), we typically look for the following:
- A translation that aligns a point from \( \triangle PBK \) to its corresponding point in \( \triangle LQA \).
- Or a rotation that fixes one point while aligning the others appropriately.
Since we don't have the visual of the triangles, let’s go through a thought process with the translations and rotations provided:
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If we were to translate along the vector so that point B maps to point A, it seems like a possible option, as it directly moves point B to point A. After obtaining the position of B at A, we would need to check if points P and K can be mapped to points L and Q correspondingly through this translation.
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A translation matching \( B \rightarrow Q \) or any other variants might not respect the symmetry and orientation needed.
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The rotation of 180° (counterclockwise) about point B would also likely alter the configuration since it would reposition the points in a way not consistent with a direct correspondence unless point B is directly between corresponding points.
In conclusion, without additional information or visual confirmation, the most straightforward rigid motion from your list that leads towards mapping one triangle to the other directly is:
Translation along the vector so that point B maps to point A.
This method allows for the adjustment while keeping the necessary congruence necessary for triangle mapping.
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