Question
What two rigid transformations were performed on figure ABCD to produce the congruent figure WXYZ ? (1 point) Responses 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 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 rotated 90° (counterclockwise), then shifted 3 units to the left and 5 units up. upper A upper B upper C upper D was first rotated 90 degrees (counterclockwise), then shifted 3 units to the left and 5 units up. ABCD was first rotated −270° (clockwise), then shifted 3 units to the left and 5 units up.
Answers
GPT-4o mini
To determine the correct sequence of transformations that produce congruent figures ABCD and WXYZ, we need to analyze the given options based on the properties of rigid transformations.
1. **Translation** (shifting): This movement slides the figure in a given direction without changing its shape or orientation.
2. **Rotation**: This turns the figure around a specific point by a certain angle.
Now let’s examine the options:
- **Option 1**: ABCD was first shifted 3 units to the left and 5 units up, then rotated 90° (counterclockwise).
- **Option 2**: ABCD was first shifted 3 units to the left and 5 units up, then rotated −90° (clockwise).
- **Option 3**: ABCD was first rotated 90° (counterclockwise), then shifted 3 units to the left and 5 units up.
- **Option 4**: ABCD was first rotated −270° (clockwise), then shifted 3 units to the left and 5 units up.
To find which option accurately describes the transformation that produces figure WXYZ from figure ABCD, we need to consider the impact of both translation and rotation:
- If the first transformation is a translation followed by a rotation, it would alter the position and orientation of the figure appropriately and is commonly used in congruent transformations.
- Similarly, if we rotate first followed by a translation, it also can yield congruency depending on the specifics of the figures involved.
Considering these insights:
Option **1** or **2** (translation first, then rotation) would typically maintain congruence, but we have to consider the direction of the rotation too.
In your case, we can't see the figures directly, but generally:
- If you're shifting (translating) a figure (3 units left, 5 units up) and then rotating it 90 degrees counterclockwise, that's a common transformation path.
Therefore, the most typical sequence to maintain congruency would often be option **1**: "ABCD was first shifted 3 units to the left and 5 units up, then rotated 90° (counterclockwise)."
If your figures and their requirements indicate a different sequence, that might alter the response, but elsewhere in rigid transformations, this response tends to hold.
1. **Translation** (shifting): This movement slides the figure in a given direction without changing its shape or orientation.
2. **Rotation**: This turns the figure around a specific point by a certain angle.
Now let’s examine the options:
- **Option 1**: ABCD was first shifted 3 units to the left and 5 units up, then rotated 90° (counterclockwise).
- **Option 2**: ABCD was first shifted 3 units to the left and 5 units up, then rotated −90° (clockwise).
- **Option 3**: ABCD was first rotated 90° (counterclockwise), then shifted 3 units to the left and 5 units up.
- **Option 4**: ABCD was first rotated −270° (clockwise), then shifted 3 units to the left and 5 units up.
To find which option accurately describes the transformation that produces figure WXYZ from figure ABCD, we need to consider the impact of both translation and rotation:
- If the first transformation is a translation followed by a rotation, it would alter the position and orientation of the figure appropriately and is commonly used in congruent transformations.
- Similarly, if we rotate first followed by a translation, it also can yield congruency depending on the specifics of the figures involved.
Considering these insights:
Option **1** or **2** (translation first, then rotation) would typically maintain congruence, but we have to consider the direction of the rotation too.
In your case, we can't see the figures directly, but generally:
- If you're shifting (translating) a figure (3 units left, 5 units up) and then rotating it 90 degrees counterclockwise, that's a common transformation path.
Therefore, the most typical sequence to maintain congruency would often be option **1**: "ABCD was first shifted 3 units to the left and 5 units up, then rotated 90° (counterclockwise)."
If your figures and their requirements indicate a different sequence, that might alter the response, but elsewhere in rigid transformations, this response tends to hold.