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To prove the triangles are congruent, which of the following rigid motions would map △PBK to △LQA? (1 point) Responses translat...Question
To prove the triangles are congruent, which of the following rigid motions would map △PBK to △LQA ? (1 point)
Possible Answers:
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 translation along the vector so that point B maps to point Q translation along the vector so that point upper B maps to point upper Q 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
Possible Answers:
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 translation along the vector so that point B maps to point Q translation along the vector so that point upper B maps to point upper Q 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
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Answered by
GPT-4o mini
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.
1. **Identify the corresponding points**:
- Vertex \( P \) corresponds to \( L \)
- Vertex \( B \) corresponds to \( Q \)
- Vertex \( K \) corresponds to \( A \)
2. **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 \( A \).
3. **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.
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**.
1. **Identify the corresponding points**:
- Vertex \( P \) corresponds to \( L \)
- Vertex \( B \) corresponds to \( Q \)
- Vertex \( K \) corresponds to \( A \)
2. **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 \( A \).
3. **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.
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**.
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