Question
Figure
\[P\] was rotated about the center shown by
\[180^\circ\].
A triangle labeled P. The solid point labeled center represents the center of rotation.
\[P\]
Which figure is the image of
\[P\]?
Choose 1 answer:
Choose 1 answer:
(Choice A) A triangle labeled P and a rotated copy of it labeled A. The solid point represents the center of rotation. The triangle is rotated to the left of center. One vertex of triangle P is at 4 o'clock, and the corresponding vertex of the rotated copy is at 10 o'clock.
\[A\]
\[P\]
A
A triangle labeled P and a rotated copy of it labeled A. The solid point represents the center of rotation. The triangle is rotated to the left of center. One vertex of triangle P is at 4 o'clock, and the corresponding vertex of the rotated copy is at 10 o'clock.
\[A\]
\[P\]
(Choice B) A triangle labeled P and a rotated copy of it labeled B. The solid point represents the center of rotation. The triangle is rotated to the left of center and shifted right. One vertex of triangle P is at 4 o'clock, and the corresponding vertex of the rotated copy is at 10 o'clock.
\[B\]
\[P\]
B
A triangle labeled P and a rotated copy of it labeled B. The solid point represents the center of rotation. The triangle is rotated to the left of center and shifted right. One vertex of triangle P is at 4 o'clock, and the corresponding vertex of the rotated copy is at 10 o'clock.
\[B\]
\[P\]
(Choice C) A triangle labeled P and a shifted copy of it labeled C. The solid point represents the center of rotation. The triangle is shifted to the left of center. One vertex of triangle P is at 2 o'clock, and the corresponding vertex of the rotated copy is at 2 o'clock.
\[C\]
\[P\]
C
A triangle labeled P and a shifted copy of it labeled C. The solid point represents the center of rotation. The triangle is shifted to the left of center. One vertex of triangle P is at 2 o'clock, and the corresponding vertex of the rotated copy is at 2 o'clock.
\[C\]
\[P\]
(Choice D) A triangle labeled P and a shifted copy of it labeled D. The solid point represents the center of rotation. The triangle is shifted to the left of center. One vertex of triangle P is at 2 o'clock, and the corresponding vertex of the rotated copy is at 2 o'clock.
\[D\]
\[P\]
D
A triangle labeled P and a shifted copy of it labeled D. The solid point represents the center of rotation. The triangle is shifted to the left of center. One vertex of triangle P is at 2 o'clock, and the corresponding vertex of the rotated copy is at 2 o'clock.
\[D\]
\[P\]
\[P\] was rotated about the center shown by
\[180^\circ\].
A triangle labeled P. The solid point labeled center represents the center of rotation.
\[P\]
Which figure is the image of
\[P\]?
Choose 1 answer:
Choose 1 answer:
(Choice A) A triangle labeled P and a rotated copy of it labeled A. The solid point represents the center of rotation. The triangle is rotated to the left of center. One vertex of triangle P is at 4 o'clock, and the corresponding vertex of the rotated copy is at 10 o'clock.
\[A\]
\[P\]
A
A triangle labeled P and a rotated copy of it labeled A. The solid point represents the center of rotation. The triangle is rotated to the left of center. One vertex of triangle P is at 4 o'clock, and the corresponding vertex of the rotated copy is at 10 o'clock.
\[A\]
\[P\]
(Choice B) A triangle labeled P and a rotated copy of it labeled B. The solid point represents the center of rotation. The triangle is rotated to the left of center and shifted right. One vertex of triangle P is at 4 o'clock, and the corresponding vertex of the rotated copy is at 10 o'clock.
\[B\]
\[P\]
B
A triangle labeled P and a rotated copy of it labeled B. The solid point represents the center of rotation. The triangle is rotated to the left of center and shifted right. One vertex of triangle P is at 4 o'clock, and the corresponding vertex of the rotated copy is at 10 o'clock.
\[B\]
\[P\]
(Choice C) A triangle labeled P and a shifted copy of it labeled C. The solid point represents the center of rotation. The triangle is shifted to the left of center. One vertex of triangle P is at 2 o'clock, and the corresponding vertex of the rotated copy is at 2 o'clock.
\[C\]
\[P\]
C
A triangle labeled P and a shifted copy of it labeled C. The solid point represents the center of rotation. The triangle is shifted to the left of center. One vertex of triangle P is at 2 o'clock, and the corresponding vertex of the rotated copy is at 2 o'clock.
\[C\]
\[P\]
(Choice D) A triangle labeled P and a shifted copy of it labeled D. The solid point represents the center of rotation. The triangle is shifted to the left of center. One vertex of triangle P is at 2 o'clock, and the corresponding vertex of the rotated copy is at 2 o'clock.
\[D\]
\[P\]
D
A triangle labeled P and a shifted copy of it labeled D. The solid point represents the center of rotation. The triangle is shifted to the left of center. One vertex of triangle P is at 2 o'clock, and the corresponding vertex of the rotated copy is at 2 o'clock.
\[D\]
\[P\]
Answers
Answered by
GPT-4o mini
To determine the correct image of triangle \( P \) after a \( 180^\circ \) rotation about the center point, we need to consider what a \( 180^\circ \) rotation entails.
1. **Understanding the Rotation**: When a figure is rotated \( 180^\circ \) about a point, every point on the figure moves directly to the opposite side of that point, at the same distance away.
2. **Visualizing Triangle P**: If one vertex of triangle \( P \) is located at 4 o'clock (which is one specific position on a clock) before the rotation, the corresponding vertex after a \( 180^\circ \) rotation will move to the opposite position on the clock, which is 10 o'clock.
3. **Analyzing the Choices**:
- **Choice A** shows triangle \( P \) and its rotated copy \( A \) accurately positioned with respect to the center of rotation, where the vertices shift precisely as expected from a \( 180^\circ \) rotation.
- **Choice B** suggests a rightward shift along with the rotation, which isn't a correct description of a simple \( 180^\circ \) rotation about a point.
- **Choice C** and **Choice D** show a scenario where the copy is simply shifted without rotation, hence they also don't represent a \( 180^\circ \) rotation.
Based on this analysis, the correct answer is:
**Choice A**: A triangle labeled \( P \) and a rotated copy of it labeled \( A \). The solid point represents the center of rotation. The triangle is rotated to the left of center. One vertex of triangle \( P \) is at 4 o'clock, and the corresponding vertex of the rotated copy is at 10 o'clock.
1. **Understanding the Rotation**: When a figure is rotated \( 180^\circ \) about a point, every point on the figure moves directly to the opposite side of that point, at the same distance away.
2. **Visualizing Triangle P**: If one vertex of triangle \( P \) is located at 4 o'clock (which is one specific position on a clock) before the rotation, the corresponding vertex after a \( 180^\circ \) rotation will move to the opposite position on the clock, which is 10 o'clock.
3. **Analyzing the Choices**:
- **Choice A** shows triangle \( P \) and its rotated copy \( A \) accurately positioned with respect to the center of rotation, where the vertices shift precisely as expected from a \( 180^\circ \) rotation.
- **Choice B** suggests a rightward shift along with the rotation, which isn't a correct description of a simple \( 180^\circ \) rotation about a point.
- **Choice C** and **Choice D** show a scenario where the copy is simply shifted without rotation, hence they also don't represent a \( 180^\circ \) rotation.
Based on this analysis, the correct answer is:
**Choice A**: A triangle labeled \( P \) and a rotated copy of it labeled \( A \). The solid point represents the center of rotation. The triangle is rotated to the left of center. One vertex of triangle \( P \) is at 4 o'clock, and the corresponding vertex of the rotated copy is at 10 o'clock.