Question
Which sequence of transformations results in figures being similar but not congruent?
Responses
A reflection across x-axis, reflection across y-axisreflection across x-axis, reflection across y-axis
B 180° clockwise rotation, translation 8 units up180° clockwise rotation, translation 8 units up
C translation 3 units left, reflection across the x-axistranslation 3 units left, reflection across the x-axis
D reflection across the y-axis, dilation with a factor of 2
Responses
A reflection across x-axis, reflection across y-axisreflection across x-axis, reflection across y-axis
B 180° clockwise rotation, translation 8 units up180° clockwise rotation, translation 8 units up
C translation 3 units left, reflection across the x-axistranslation 3 units left, reflection across the x-axis
D reflection across the y-axis, dilation with a factor of 2
Answers
GPT-4o mini
The correct response is:
**D) reflection across the y-axis, dilation with a factor of 2**
This sequence results in figures being similar but not congruent because a dilation (enlargement or reduction) changes the size of the figure while maintaining its shape. A reflection will flip the figure over the y-axis, but the dilation with a factor of 2 will increase the size, making the figures similar (same shape) but not congruent (not the same size).
**D) reflection across the y-axis, dilation with a factor of 2**
This sequence results in figures being similar but not congruent because a dilation (enlargement or reduction) changes the size of the figure while maintaining its shape. A reflection will flip the figure over the y-axis, but the dilation with a factor of 2 will increase the size, making the figures similar (same shape) but not congruent (not the same size).