Question
Which sequence of transformations results in figures being similar but not congruent?
Responses
A reflection across x-axis, translation 8 units left,reflection across x-axis, translation 8 units left,
B 180° clockwise rotation, translation 7 units down180° clockwise rotation, translation 7 units down
C reflection across y-axis, reflection across the x-axisreflection across y-axis, reflection across the x-axis
D 90° clockwise rotation, dilation with a factor of 1/2
Responses
A reflection across x-axis, translation 8 units left,reflection across x-axis, translation 8 units left,
B 180° clockwise rotation, translation 7 units down180° clockwise rotation, translation 7 units down
C reflection across y-axis, reflection across the x-axisreflection across y-axis, reflection across the x-axis
D 90° clockwise rotation, dilation with a factor of 1/2
Answers
GPT-4o mini
To determine which sequence of transformations results in figures that are similar but not congruent, we need to look for a transformation that alters the size but maintains the shape of the figure.
- **A**: Reflection across the x-axis, followed by a translation does not change the size of the figures, so this will produce congruent figures.
- **B**: A 180° rotation followed by a translation does not change the size, resulting in congruent figures.
- **C**: Reflections across the y-axis and x-axis (either in sequence or simultaneously) will also not change the size, resulting in congruent figures.
- **D**: A 90° clockwise rotation followed by a dilation with a factor of 1/2 will change both the orientation and the size of the figure. The dilation will reduce the size of the figure, making it similar but not congruent to the original figure.
Thus, the correct answer is **D**: 90° clockwise rotation, dilation with a factor of 1/2.
- **A**: Reflection across the x-axis, followed by a translation does not change the size of the figures, so this will produce congruent figures.
- **B**: A 180° rotation followed by a translation does not change the size, resulting in congruent figures.
- **C**: Reflections across the y-axis and x-axis (either in sequence or simultaneously) will also not change the size, resulting in congruent figures.
- **D**: A 90° clockwise rotation followed by a dilation with a factor of 1/2 will change both the orientation and the size of the figure. The dilation will reduce the size of the figure, making it similar but not congruent to the original figure.
Thus, the correct answer is **D**: 90° clockwise rotation, dilation with a factor of 1/2.