# Select all transformations that must result in a congruent image

Posted By Admin @ September 03, 2022

#### Question:

Need help with this

A sequence of transformations is performed on a figure. Select all the sequences of transformations that would result in a congruent figure.
1. a translation, then a reflection
2. a rotation, then a dilation
3. a rotation, then a reflection
4, a rotation, then a rotation
5. a dilation, then a reflection
6. a rotation, then a translation
i think that it is 3 + 4

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.

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