Question
Figure
\[Q\] was rotated about the center shown by
\[270^\circ\] counterclockwise.
A triangle labeled Q. The solid point labeled center represents the center of rotation.
\[Q\]
Which figure is the image of
\[Q\]?
Choose 1 answer:
Choose 1 answer:
(Choice A) A triangle labeled Q 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 Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 5 o'clock.
\[A\]
\[Q\]
A
A triangle labeled Q 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 Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 5 o'clock.
\[A\]
\[Q\]
(Choice B) A triangle labeled Q and a rotated copy of it labeled B. The solid point represents the center of rotation. The triangle is rotated to the right of center. One vertex of triangle Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 11 o'clock.
\[B\]
\[Q\]
B
A triangle labeled Q and a rotated copy of it labeled B. The solid point represents the center of rotation. The triangle is rotated to the right of center. One vertex of triangle Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 11 o'clock.
\[B\]
\[Q\]
(Choice C) A triangle labeled Q 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 Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 8 o'clock.
\[C\]
\[Q\]
C
A triangle labeled Q 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 Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 8 o'clock.
\[C\]
\[Q\]
(Choice D) A triangle labeled Q and a shifted copy of it labeled D. The solid point represents the center of rotation. The triangle is shifted to the down. One vertex of triangle Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 8 o'clock.
\[D\]
\[Q\]
D
A triangle labeled Q and a shifted copy of it labeled D. The solid point represents the center of rotation. The triangle is shifted to the down. One vertex of triangle Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 8 o'clock.
\[D\]
\[Q\]
\[Q\] was rotated about the center shown by
\[270^\circ\] counterclockwise.
A triangle labeled Q. The solid point labeled center represents the center of rotation.
\[Q\]
Which figure is the image of
\[Q\]?
Choose 1 answer:
Choose 1 answer:
(Choice A) A triangle labeled Q 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 Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 5 o'clock.
\[A\]
\[Q\]
A
A triangle labeled Q 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 Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 5 o'clock.
\[A\]
\[Q\]
(Choice B) A triangle labeled Q and a rotated copy of it labeled B. The solid point represents the center of rotation. The triangle is rotated to the right of center. One vertex of triangle Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 11 o'clock.
\[B\]
\[Q\]
B
A triangle labeled Q and a rotated copy of it labeled B. The solid point represents the center of rotation. The triangle is rotated to the right of center. One vertex of triangle Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 11 o'clock.
\[B\]
\[Q\]
(Choice C) A triangle labeled Q 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 Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 8 o'clock.
\[C\]
\[Q\]
C
A triangle labeled Q 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 Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 8 o'clock.
\[C\]
\[Q\]
(Choice D) A triangle labeled Q and a shifted copy of it labeled D. The solid point represents the center of rotation. The triangle is shifted to the down. One vertex of triangle Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 8 o'clock.
\[D\]
\[Q\]
D
A triangle labeled Q and a shifted copy of it labeled D. The solid point represents the center of rotation. The triangle is shifted to the down. One vertex of triangle Q is at 8 o'clock, and the corresponding vertex of the rotated copy is at 8 o'clock.
\[D\]
\[Q\]
Answers
Answered by
GPT-4o mini
To find the correct image of triangle \( Q \) after a \( 270^\circ \) counterclockwise rotation around the center point, we need to visualize how the vertices of the triangle will move.
1. **Understanding \( 270^\circ \) Counterclockwise Rotation:**
- A \( 270^\circ \) counterclockwise rotation is equivalent to a \( 90^\circ \) clockwise rotation.
- If a vertex of the triangle is at the position of 8 o'clock before rotation, after a \( 90^\circ \) clockwise rotation, it will move to the position of 10 o'clock (i.e., 90 degrees from 8 o'clock clockwise).
2. **Applying this to the Options:**
- **Choice A:** One vertex of triangle \( Q \) is at 8 o'clock, and the corresponding vertex of the rotated copy is at 5 o'clock. (This is incorrect; it should go to 10 o'clock).
- **Choice B:** One vertex of triangle \( Q \) is at 8 o'clock, and the corresponding vertex of the rotated copy is at 11 o'clock. (This is incorrect; it should also go to 10 o'clock).
- **Choice C:** One vertex of triangle \( Q \) is at 8 o'clock, and the corresponding vertex of the rotated copy is still at 8 o'clock. (This is incorrect; it has not rotated).
- **Choice D:** One vertex of triangle \( Q \) is at 8 o'clock, and the corresponding vertex of the rotated copy is also at 8 o'clock. (Also incorrect; the same reason as Choice C).
None of the choices seem to be entirely correct based on the expected outcome of the rotation. However, we would expect the correct image after rotation to position a vertex originally at 8 o'clock to now be positioned at 10 o'clock. Therefore, if we had a choice that indicated movement to 10 o'clock, that would be the correct answer, but it seems none of the provided options accurately reflect this.
If you need to answer among these given options, there appears to be an error because all choices fail to show the correct rotation outcome.
1. **Understanding \( 270^\circ \) Counterclockwise Rotation:**
- A \( 270^\circ \) counterclockwise rotation is equivalent to a \( 90^\circ \) clockwise rotation.
- If a vertex of the triangle is at the position of 8 o'clock before rotation, after a \( 90^\circ \) clockwise rotation, it will move to the position of 10 o'clock (i.e., 90 degrees from 8 o'clock clockwise).
2. **Applying this to the Options:**
- **Choice A:** One vertex of triangle \( Q \) is at 8 o'clock, and the corresponding vertex of the rotated copy is at 5 o'clock. (This is incorrect; it should go to 10 o'clock).
- **Choice B:** One vertex of triangle \( Q \) is at 8 o'clock, and the corresponding vertex of the rotated copy is at 11 o'clock. (This is incorrect; it should also go to 10 o'clock).
- **Choice C:** One vertex of triangle \( Q \) is at 8 o'clock, and the corresponding vertex of the rotated copy is still at 8 o'clock. (This is incorrect; it has not rotated).
- **Choice D:** One vertex of triangle \( Q \) is at 8 o'clock, and the corresponding vertex of the rotated copy is also at 8 o'clock. (Also incorrect; the same reason as Choice C).
None of the choices seem to be entirely correct based on the expected outcome of the rotation. However, we would expect the correct image after rotation to position a vertex originally at 8 o'clock to now be positioned at 10 o'clock. Therefore, if we had a choice that indicated movement to 10 o'clock, that would be the correct answer, but it seems none of the provided options accurately reflect this.
If you need to answer among these given options, there appears to be an error because all choices fail to show the correct rotation outcome.