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

Step-by-step 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.