Question
A coordinate plane's x-axis ranges from negative 8 to 0 and its y-axis ranges from negative 6 to 10, both by 1-unit increments. Points upper L, upper O, upper W, upper L prime, upper O prime, and upper W prime are plotted forming two triangles.
ΔLOW→ΔL"O"W" looks like a translation. What two moves could replace the one translation?
(1 point)
Responses
a reflection across parallel lines
a reflection across parallel lines
a reflection across intersecting lines
a reflection across intersecting lines
a reflection across perpendicular lines
a reflection across perpendicular lines
a counterclockwise rotation of 180 degrees
ΔLOW→ΔL"O"W" looks like a translation. What two moves could replace the one translation?
(1 point)
Responses
a reflection across parallel lines
a reflection across parallel lines
a reflection across intersecting lines
a reflection across intersecting lines
a reflection across perpendicular lines
a reflection across perpendicular lines
a counterclockwise rotation of 180 degrees
Answers
GPT-4o mini
To determine what two moves could replace the translation from triangle ΔLOW to triangle ΔL"O"W", we need to analyze the positions of the points and the nature of the transformation.
Given that triangles formed by points are involved, translated triangles are often the result of either a combination of rotations and reflections or two distinct reflections. Since a translation simply shifts a shape without altering its orientation or size, two reflections (whether across parallel lines, intersecting lines, or perpendicular lines) can effectively produce the same outcome.
Among the options provided:
1. **A reflection across parallel lines** - This option involves moving a shape by reflecting it across two lines that are parallel to each other. This result could also replicate a translation if done correctly.
2. **A reflection across intersecting lines** - This option would typically alter the shape's orientation more significantly. It is less likely to produce a simple translation result.
3. **A reflection across perpendicular lines** - Like the previous option, this choice would significantly change the orientation of the triangle rather than keeping it aligned as in a translation.
4. **A counterclockwise rotation of 180 degrees** - This transformation changes the orientation of the triangle and does not count as a translation.
The best answer among the choices would be:
**A reflection across parallel lines**.
This option would allow for the translation to be effectively realized as taking place through two moves, maintaining the orientation and relative position of the original triangles involved. Therefore, two reflections across parallel lines could replace one translation.
Given that triangles formed by points are involved, translated triangles are often the result of either a combination of rotations and reflections or two distinct reflections. Since a translation simply shifts a shape without altering its orientation or size, two reflections (whether across parallel lines, intersecting lines, or perpendicular lines) can effectively produce the same outcome.
Among the options provided:
1. **A reflection across parallel lines** - This option involves moving a shape by reflecting it across two lines that are parallel to each other. This result could also replicate a translation if done correctly.
2. **A reflection across intersecting lines** - This option would typically alter the shape's orientation more significantly. It is less likely to produce a simple translation result.
3. **A reflection across perpendicular lines** - Like the previous option, this choice would significantly change the orientation of the triangle rather than keeping it aligned as in a translation.
4. **A counterclockwise rotation of 180 degrees** - This transformation changes the orientation of the triangle and does not count as a translation.
The best answer among the choices would be:
**A reflection across parallel lines**.
This option would allow for the translation to be effectively realized as taking place through two moves, maintaining the orientation and relative position of the original triangles involved. Therefore, two reflections across parallel lines could replace one translation.