Answer: A. a reflection across the y-axis followed by a dilation with a scale factor of 0.5
D. a dilation with a scale factor of 2 followed by a reflection across the x-axis
Explanation:
Let's check all the options.
A. a reflection across the y-axis followed by a dilation with a scale factor of 0.5
Here first transformation is reflection which is a rigid transformation that produces only congruent images.
But dilation is not a rigid transformation, it produces similar images but not produce congruent images if the value of scale factor is other than 1.
Hence, this sequence of transformations would result in a figure that is similar, but not congruent, to the original figure.
B. a translation 2 units up followed by a rotation of 180° about the origin
Here both the transformations are rigid transformations that produces only congruent images.
C. a rotation about the origin of 25° followed by a reflection across the y-axis
Here both the transformations are rigid transformations that produces only congruent images.
D. a dilation with a scale factor of 2 followed by a reflection across the x-axis
Here second transformation is reflection which is a rigid transformation that produces only congruent images.
But the first transformation i.e. dilation is not a rigid transformation, it produces similar images but not produce congruent images if the value of scale factor is other than 1.
Hence, this sequence of transformations would result in a figure that is similar, but not congruent, to the original figure.