Question
What two rigid transformations were performed on figure ABCD
to produce the congruent figure WXYZ
?
(1 point)
Responses
ABCD
was first rotated −270°
(clockwise), then shifted 3 units to the left and 5 units up.
upper A upper B upper C upper D was first rotated negative 270 degrees (clockwise), then shifted 3 units to the left and 5 units up.
ABCD
was first shifted 3 units to the left and 5 units up, then rotated −90°
(clockwise).
upper A upper B upper C upper D was first shifted 3 units to the left and 5 units up, then rotated negative 90 degrees (clockwise).
ABCD
was first shifted 3 units to the left and 5 units up, then rotated 90°
(counterclockwise).
upper A upper B upper C upper D was first shifted 3 units to the left and 5 units up, then rotated 90 degrees (counterclockwise).
ABCD
was first rotated 90°
(counterclockwise), then shifted 3 units to the left and 5 units up.
to produce the congruent figure WXYZ
?
(1 point)
Responses
ABCD
was first rotated −270°
(clockwise), then shifted 3 units to the left and 5 units up.
upper A upper B upper C upper D was first rotated negative 270 degrees (clockwise), then shifted 3 units to the left and 5 units up.
ABCD
was first shifted 3 units to the left and 5 units up, then rotated −90°
(clockwise).
upper A upper B upper C upper D was first shifted 3 units to the left and 5 units up, then rotated negative 90 degrees (clockwise).
ABCD
was first shifted 3 units to the left and 5 units up, then rotated 90°
(counterclockwise).
upper A upper B upper C upper D was first shifted 3 units to the left and 5 units up, then rotated 90 degrees (counterclockwise).
ABCD
was first rotated 90°
(counterclockwise), then shifted 3 units to the left and 5 units up.
Answers
GPT-4o mini
To determine the correct sequence of rigid transformations that were performed on figure ABCD to produce congruent figure WXYZ, we need to understand the effects of these transformations:
1. **Rotation** refers to turning the figure around a point (typically the origin) by a specified angle.
2. **Translation** (or shifting) moves the figure in a specific direction without changing its shape or size.
Let's analyze the provided options:
- **First Option**: Rotated -270° (which is equivalent to a 90° clockwise rotation) then shifted. This could work if it fits the transition from ABCD to WXYZ.
- **Second Option**: Shifted then rotated -90° (which is a 90° clockwise rotation). This seems plausible.
- **Third Option**: Shifted then rotated 90° (counterclockwise). This also could be true, but contradicts the orientation needed if WXYZ is a reflection or similar change in direction.
- **Fourth Option**: Rotated 90° counterclockwise then shifted. This may not match perfectly regarding the shift afterward.
Without a visual representation, it’s challenging to specify definitively. However, both the second and third options have a potential tracking path considering one shifts first and then rotates. To finalize, if WXYZ requires a turn that isn't a complete congruence post shift, consider the orientation needed against the shifts given in options.
**Final Answer**: Would likely lean towards:
- **ABCD was first shifted 3 units to the left and 5 units up, then rotated -90° (clockwise).**
But double-check actual figure orientations in your reference for full verification against what transformation needed matches correctly.
1. **Rotation** refers to turning the figure around a point (typically the origin) by a specified angle.
2. **Translation** (or shifting) moves the figure in a specific direction without changing its shape or size.
Let's analyze the provided options:
- **First Option**: Rotated -270° (which is equivalent to a 90° clockwise rotation) then shifted. This could work if it fits the transition from ABCD to WXYZ.
- **Second Option**: Shifted then rotated -90° (which is a 90° clockwise rotation). This seems plausible.
- **Third Option**: Shifted then rotated 90° (counterclockwise). This also could be true, but contradicts the orientation needed if WXYZ is a reflection or similar change in direction.
- **Fourth Option**: Rotated 90° counterclockwise then shifted. This may not match perfectly regarding the shift afterward.
Without a visual representation, it’s challenging to specify definitively. However, both the second and third options have a potential tracking path considering one shifts first and then rotates. To finalize, if WXYZ requires a turn that isn't a complete congruence post shift, consider the orientation needed against the shifts given in options.
**Final Answer**: Would likely lean towards:
- **ABCD was first shifted 3 units to the left and 5 units up, then rotated -90° (clockwise).**
But double-check actual figure orientations in your reference for full verification against what transformation needed matches correctly.