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

1 answer

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.