Question
Which rigid transformation could be defined as a turn around a center point determined by an angle measured in degrees?(1 point)
Responses
a rotation
a rotation
a dilation
a dilation
a reflection
a reflection
a translation
Use the image to answer the question.
Beneath a cloudy sky, a large body of water is shown with mountains on either side and in the distance. Mirror images of the mountains can be seen in the water. Several trees line the water bank.
Source: Joe Dunckley/Shutterstock
This image could be used to help create a definition for which of the following?
(1 point)
Responses
rotation
rotation
reflection
reflection
dilation
dilation
translation
Which graph demonstrates a transformation that preserves both distance and angle measure?(1 point)
Responses
Two squares, a smaller one inside a larger one, are plotted in quadrant 1 of a coordinate plane. The smaller square shares a vertex and two of its sides with parts of two sides of the larger square. The x- and y-axis both range from 0 to 8 in increments of 1.
Image with alt text: Two squares, a smaller one inside a larger one, are plotted in quadrant 1 of a coordinate plane. The smaller square shares a vertex and two of its sides with parts of two sides of the larger square. The x- and y-axis both range from 0 to 8 in increments of 1.
Two equivalent triangles are plotted on a coordinate plane, one in quadrant 1 and one that starts in quadrant 2 and crosses into quadrant 1. The x-axis ranges from negative 4 to 7 in increments of 1, and the y-axis ranges from 0 to 7 in increments of 1. A line connects a vertex of the triangle in quadrant 2 to the matching vertex of the triangle in quadrant 1.
Image with alt text: Two equivalent triangles are plotted on a coordinate plane, one in quadrant 1 and one that starts in quadrant 2 and crosses into quadrant 1. The x-axis ranges from negative 4 to 7 in increments of 1, and the y-axis ranges from 0 to 7 in increments of 1. A line connects a vertex of the triangle in quadrant 2 to the matching vertex of the triangle in quadrant 1.
Two triangles of different sizes are plotted on a coordinate plane. The x-axis ranges from negative 4 to 8 in increments of 1, and the y-axis ranges from negative 4 to 10 in increments of 1.The larger triangle is plotted around the origin and extends into all four quadrants, and the smaller triangle extends between quadrants 1 and 2.
Image with alt text: Two triangles of different sizes are plotted on a coordinate plane. The x-axis ranges from negative 4 to 8 in increments of 1, and the y-axis ranges from negative 4 to 10 in increments of 1.The larger triangle is plotted around the origin and extends into all four quadrants, and the smaller triangle extends between quadrants 1 and 2.
Two rectangles, a smaller one inside a larger one, are plotted around the origin on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 3 to 5 in increments of 1.
Image with alt text: Two rectangles, a smaller one inside a larger one, are plotted around the origin on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 3 to 5 in increments of 1.
Skip to navigation
Question
△EFG is rotated −90 degrees (clockwise) to create △XYZ . Which of the following statements must be true?(1 point)
Responses
EG¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯
Modifying above upper E upper G with bar congruent to Modifying above upper X upper Y with bar
EF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯
Modifying above upper E upper F with bar congruent to Modifying above upper X upper Z with bar
∠F≅∠Z
angle upper F congruent to angle upper Z
∠E≅∠X
angle upper E congruent to angle upper X
Skip to navigation
Talia is playing with a plastic hoop that she spins around her waist. The spinning hoop resembles a(1 point)
Responses
rotation.
rotation.
dilation.
dilation.
reflection.
reflection.
translation.
Responses
a rotation
a rotation
a dilation
a dilation
a reflection
a reflection
a translation
Use the image to answer the question.
Beneath a cloudy sky, a large body of water is shown with mountains on either side and in the distance. Mirror images of the mountains can be seen in the water. Several trees line the water bank.
Source: Joe Dunckley/Shutterstock
This image could be used to help create a definition for which of the following?
(1 point)
Responses
rotation
rotation
reflection
reflection
dilation
dilation
translation
Which graph demonstrates a transformation that preserves both distance and angle measure?(1 point)
Responses
Two squares, a smaller one inside a larger one, are plotted in quadrant 1 of a coordinate plane. The smaller square shares a vertex and two of its sides with parts of two sides of the larger square. The x- and y-axis both range from 0 to 8 in increments of 1.
Image with alt text: Two squares, a smaller one inside a larger one, are plotted in quadrant 1 of a coordinate plane. The smaller square shares a vertex and two of its sides with parts of two sides of the larger square. The x- and y-axis both range from 0 to 8 in increments of 1.
Two equivalent triangles are plotted on a coordinate plane, one in quadrant 1 and one that starts in quadrant 2 and crosses into quadrant 1. The x-axis ranges from negative 4 to 7 in increments of 1, and the y-axis ranges from 0 to 7 in increments of 1. A line connects a vertex of the triangle in quadrant 2 to the matching vertex of the triangle in quadrant 1.
Image with alt text: Two equivalent triangles are plotted on a coordinate plane, one in quadrant 1 and one that starts in quadrant 2 and crosses into quadrant 1. The x-axis ranges from negative 4 to 7 in increments of 1, and the y-axis ranges from 0 to 7 in increments of 1. A line connects a vertex of the triangle in quadrant 2 to the matching vertex of the triangle in quadrant 1.
Two triangles of different sizes are plotted on a coordinate plane. The x-axis ranges from negative 4 to 8 in increments of 1, and the y-axis ranges from negative 4 to 10 in increments of 1.The larger triangle is plotted around the origin and extends into all four quadrants, and the smaller triangle extends between quadrants 1 and 2.
Image with alt text: Two triangles of different sizes are plotted on a coordinate plane. The x-axis ranges from negative 4 to 8 in increments of 1, and the y-axis ranges from negative 4 to 10 in increments of 1.The larger triangle is plotted around the origin and extends into all four quadrants, and the smaller triangle extends between quadrants 1 and 2.
Two rectangles, a smaller one inside a larger one, are plotted around the origin on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 3 to 5 in increments of 1.
Image with alt text: Two rectangles, a smaller one inside a larger one, are plotted around the origin on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 3 to 5 in increments of 1.
Skip to navigation
Question
△EFG is rotated −90 degrees (clockwise) to create △XYZ . Which of the following statements must be true?(1 point)
Responses
EG¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯
Modifying above upper E upper G with bar congruent to Modifying above upper X upper Y with bar
EF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯
Modifying above upper E upper F with bar congruent to Modifying above upper X upper Z with bar
∠F≅∠Z
angle upper F congruent to angle upper Z
∠E≅∠X
angle upper E congruent to angle upper X
Skip to navigation
Talia is playing with a plastic hoop that she spins around her waist. The spinning hoop resembles a(1 point)
Responses
rotation.
rotation.
dilation.
dilation.
reflection.
reflection.
translation.
Answers
GPT-4o mini
Here are the answers to the questions based on the provided context:
1. **Which rigid transformation could be defined as a turn around a center point determined by an angle measured in degrees?**
- **Response:** a rotation
2. **This image could be used to help create a definition for which of the following?**
- **Response:** reflection (since the mirror images of the mountains could illustrate the concept of reflection).
3. **Which graph demonstrates a transformation that preserves both distance and angle measure?**
- **Response:** Two rectangles, a smaller one inside a larger one, are plotted around the origin on a coordinate plane. (This would indicate congruence and maintain distance and angle measure).
4. **△EFG is rotated -90 degrees (clockwise) to create △XYZ. Which of the following statements must be true?**
- **Response:** ∠F≅∠Z (because corresponding angles remain congruent under rotation).
5. **Talia is playing with a plastic hoop that she spins around her waist. The spinning hoop resembles a**
- **Response:** rotation.
These answers correspond to common concepts in geometry related to transformations.
1. **Which rigid transformation could be defined as a turn around a center point determined by an angle measured in degrees?**
- **Response:** a rotation
2. **This image could be used to help create a definition for which of the following?**
- **Response:** reflection (since the mirror images of the mountains could illustrate the concept of reflection).
3. **Which graph demonstrates a transformation that preserves both distance and angle measure?**
- **Response:** Two rectangles, a smaller one inside a larger one, are plotted around the origin on a coordinate plane. (This would indicate congruence and maintain distance and angle measure).
4. **△EFG is rotated -90 degrees (clockwise) to create △XYZ. Which of the following statements must be true?**
- **Response:** ∠F≅∠Z (because corresponding angles remain congruent under rotation).
5. **Talia is playing with a plastic hoop that she spins around her waist. The spinning hoop resembles a**
- **Response:** rotation.
These answers correspond to common concepts in geometry related to transformations.