Question
Congruent figures M and M’ are shown on the coordinate grid below.
Describe a sequence of transformations on rectangle M that would result in figure M’?
Responses
A Reflection over the y axis, then translation up 5 units.
Reflection over the y axis, then translation up 5 units.
B Reflection over the y axis, then translation down 5 units.Reflection over the y axis, then translation down 5 units.
C Reflection over the x axis, then translation up 5 units.Reflection over the x axis, then translation up 5 units.
D Reflection over the x axis, then translation down 5 units.Reflection over the x axis, then translation down 5 units.
Describe a sequence of transformations on rectangle M that would result in figure M’?
Responses
A Reflection over the y axis, then translation up 5 units.
Reflection over the y axis, then translation up 5 units.
B Reflection over the y axis, then translation down 5 units.Reflection over the y axis, then translation down 5 units.
C Reflection over the x axis, then translation up 5 units.Reflection over the x axis, then translation up 5 units.
D Reflection over the x axis, then translation down 5 units.Reflection over the x axis, then translation down 5 units.
Answers
GPT-4o mini
To determine the correct sequence of transformations that maps rectangle M onto rectangle M', we need to analyze the positions of the rectangles on the coordinate grid.
Here’s how to approach the problem:
1. **Identify the orientation and position of rectangle M**: Look at the coordinates of the corners of rectangle M and visualize where it lies on the grid.
2. **Identify the position of rectangle M'**: Look at the coordinates of M' and note how it differs from M.
3. **Determine the transformations**: Consider the effects of reflections (over the x-axis and y-axis) and translations (up or down).
**Reflection over the x-axis** would change the y-coordinates of the rectangle, while **reflection over the y-axis** would change the x-coordinates. Translations will move the rectangle up or down based on the specified number of units.
Since I don't have access to the specific coordinates or images of M and M', please apply the above steps using the data you have (the locations of M and M') to determine which sequence of transformations would accurately map M to M'.
However, based on the provided options:
- **Choice A**: Reflection over the y-axis, then translation up 5 units.
- **Choice B**: Reflection over the y-axis, then translation down 5 units.
- **Choice C**: Reflection over the x-axis, then translation up 5 units.
- **Choice D**: Reflection over the x-axis, then translation down 5 units.
Evaluate each option based on the position of M and M' after the transformations and choose the option that accurately describes the sequence leading to M'. If after a reflection, if M’ is directly above M, you might need to translate up; if it's below, you might translate down.
Adjust for movements based on your analysis!
Here’s how to approach the problem:
1. **Identify the orientation and position of rectangle M**: Look at the coordinates of the corners of rectangle M and visualize where it lies on the grid.
2. **Identify the position of rectangle M'**: Look at the coordinates of M' and note how it differs from M.
3. **Determine the transformations**: Consider the effects of reflections (over the x-axis and y-axis) and translations (up or down).
**Reflection over the x-axis** would change the y-coordinates of the rectangle, while **reflection over the y-axis** would change the x-coordinates. Translations will move the rectangle up or down based on the specified number of units.
Since I don't have access to the specific coordinates or images of M and M', please apply the above steps using the data you have (the locations of M and M') to determine which sequence of transformations would accurately map M to M'.
However, based on the provided options:
- **Choice A**: Reflection over the y-axis, then translation up 5 units.
- **Choice B**: Reflection over the y-axis, then translation down 5 units.
- **Choice C**: Reflection over the x-axis, then translation up 5 units.
- **Choice D**: Reflection over the x-axis, then translation down 5 units.
Evaluate each option based on the position of M and M' after the transformations and choose the option that accurately describes the sequence leading to M'. If after a reflection, if M’ is directly above M, you might need to translate up; if it's below, you might translate down.
Adjust for movements based on your analysis!