Question
A triangle with vertices at (1,1), (4,1), and (1,3) is transformed to a triangle with vertices at (3,1), (6,1), and (3,3). Which transformation was applied?
1 point
Translation 2 units to the right
Reflection over the y-axis
Translation 2 units up
A triangle with vertices at (2,3), (3,5), and (5,3) is transformed to a triangle with vertices at (4,6), (5,8), and (7,6). Which transformation was applied?
1 point
Translation 3 units up and 2 units right
Translation 2 units up and 2 units left
A square with vertices at (3,3), (6,3), (6,6), and (3,6) is transformed to a square with vertices at (−3,−3), (−6,−3), (−6,−6), and (−3,−6). Which transformation was applied?
1 point
Translation 6 units left and 6 units down
Rotation 180 degrees about the origin
Rotation 90 degrees clockwise about the originion 3
A pentagon with vertices at (1,1), (2,3), (4,3), (5,1), and (3,0) is transformed to a pentagon with vertices at (1,−1), (2,−3), (4,−3), (5,−1), and (3,0). Which transformation was applied?
1 point
Rotation 180 degrees about the origin
Reflection over the x-axis
A rectangle with vertices at (2,3), (5,3), (5,6), and (2,6) is transformed to a rectangle with vertices at (2,−3), (5,−3), (5,−6), and (2,−6). Which transformation was applied?
1 point
Reflection over the x-axis
Reflection over the y-axis
Translation 6 units down
1 point
Translation 2 units to the right
Reflection over the y-axis
Translation 2 units up
A triangle with vertices at (2,3), (3,5), and (5,3) is transformed to a triangle with vertices at (4,6), (5,8), and (7,6). Which transformation was applied?
1 point
Translation 3 units up and 2 units right
Translation 2 units up and 2 units left
A square with vertices at (3,3), (6,3), (6,6), and (3,6) is transformed to a square with vertices at (−3,−3), (−6,−3), (−6,−6), and (−3,−6). Which transformation was applied?
1 point
Translation 6 units left and 6 units down
Rotation 180 degrees about the origin
Rotation 90 degrees clockwise about the originion 3
A pentagon with vertices at (1,1), (2,3), (4,3), (5,1), and (3,0) is transformed to a pentagon with vertices at (1,−1), (2,−3), (4,−3), (5,−1), and (3,0). Which transformation was applied?
1 point
Rotation 180 degrees about the origin
Reflection over the x-axis
A rectangle with vertices at (2,3), (5,3), (5,6), and (2,6) is transformed to a rectangle with vertices at (2,−3), (5,−3), (5,−6), and (2,−6). Which transformation was applied?
1 point
Reflection over the x-axis
Reflection over the y-axis
Translation 6 units down
Answers
GPT-4o mini
Let's analyze each transformation one by one:
1. **Triangle Transformation from (1,1), (4,1), (1,3) to (3,1), (6,1), (3,3)**:
- The first triangle's vertices can be translated to the right by 2 units to reach the new vertices.
- Thus, the correct transformation is **Translation 2 units to the right**.
2. **Triangle Transformation from (2,3), (3,5), (5,3) to (4,6), (5,8), (7,6)**:
- The new vertices can be obtained by translating the original vertices 2 units to the right (from x-coordinates of 2 to 4, 3 to 5, and 5 to 7) and 3 units up (from y-coordinates of 3 to 6, 5 to 8).
- Thus, the correct transformation is **Translation 3 units up and 2 units right**.
3. **Square Transformation from (3,3), (6,3), (6,6), (3,6) to (−3,−3), (−6,−3), (−6,−6), (−3,−6)**:
- The original square's vertices are rotated 180 degrees about the origin, changing their signs.
- Thus, the correct transformation is **Rotation 180 degrees about the origin**.
4. **Pentagon Transformation from (1,1), (2,3), (4,3), (5,1), and (3,0) to (1,−1), (2,−3), (4,−3), (5,−1), and (3,0)**:
- The new vertices suggest that the original vertices have been reflected across the x-axis, thus changing their y-coordinates to their negatives while the x-coordinates remain unchanged.
- Therefore, the correct transformation is **Reflection over the x-axis**.
5. **Rectangle Transformation from (2,3), (5,3), (5,6), (2,6) to (2,−3), (5,−3), (5,−6), (2,−6)**:
- Similar to the pentagon transformation, the new vertices indicate that the original rectangle has also been reflected across the x-axis.
- Thus, the correct transformation is **Reflection over the x-axis**.
In summary:
1. Translation 2 units to the right
2. Translation 3 units up and 2 units right
3. Rotation 180 degrees about the origin
4. Reflection over the x-axis
5. Reflection over the x-axis
1. **Triangle Transformation from (1,1), (4,1), (1,3) to (3,1), (6,1), (3,3)**:
- The first triangle's vertices can be translated to the right by 2 units to reach the new vertices.
- Thus, the correct transformation is **Translation 2 units to the right**.
2. **Triangle Transformation from (2,3), (3,5), (5,3) to (4,6), (5,8), (7,6)**:
- The new vertices can be obtained by translating the original vertices 2 units to the right (from x-coordinates of 2 to 4, 3 to 5, and 5 to 7) and 3 units up (from y-coordinates of 3 to 6, 5 to 8).
- Thus, the correct transformation is **Translation 3 units up and 2 units right**.
3. **Square Transformation from (3,3), (6,3), (6,6), (3,6) to (−3,−3), (−6,−3), (−6,−6), (−3,−6)**:
- The original square's vertices are rotated 180 degrees about the origin, changing their signs.
- Thus, the correct transformation is **Rotation 180 degrees about the origin**.
4. **Pentagon Transformation from (1,1), (2,3), (4,3), (5,1), and (3,0) to (1,−1), (2,−3), (4,−3), (5,−1), and (3,0)**:
- The new vertices suggest that the original vertices have been reflected across the x-axis, thus changing their y-coordinates to their negatives while the x-coordinates remain unchanged.
- Therefore, the correct transformation is **Reflection over the x-axis**.
5. **Rectangle Transformation from (2,3), (5,3), (5,6), (2,6) to (2,−3), (5,−3), (5,−6), (2,−6)**:
- Similar to the pentagon transformation, the new vertices indicate that the original rectangle has also been reflected across the x-axis.
- Thus, the correct transformation is **Reflection over the x-axis**.
In summary:
1. Translation 2 units to the right
2. Translation 3 units up and 2 units right
3. Rotation 180 degrees about the origin
4. Reflection over the x-axis
5. Reflection over the x-axis