To determine which of the following does not describe a rigid motion transformation, we need to understand what a rigid motion transformation entails. A rigid motion transformation preserves the distance and angles, meaning the shape and size of the figure do not change.
Let's analyze each option:
A. Dilating a figure by a scale factor of [tex]\(\frac{1}{4}\)[/tex]:
- Dilation involves resizing the figure. When you apply a scale factor of [tex]\(\frac{1}{4}\)[/tex], every distance within the figure is reduced to one-fourth of its original length. This changes the size of the figure, meaning dilation is not a rigid motion transformation because it does not preserve the size of the figure.
B. Reflecting a figure across the [tex]\(x\)[/tex]-axis:
- Reflection is a type of rigid motion. Reflecting a figure across the [tex]\(x\)[/tex]-axis flips the figure over the axis, but it preserves the size and shape of the figure. All distances and angles within the figure remain the same. Thus, reflection is a rigid motion transformation.
C. Translating a figure 5 units right:
- Translation moves every point of a figure the same distance in a given direction. Translating a figure 5 units to the right does not alter the size or shape of the figure. All distances and angles are preserved. Hence, translation is a rigid motion transformation.
D. Rotating a figure 90 degrees:
- Rotation turns the figure around a fixed point, typically the origin, by a specified angle. Rotating a figure 90 degrees changes its orientation but keeps its shape and size unchanged. All distances and angles within the figure remain the same. Therefore, rotation is a rigid motion transformation.
In conclusion, the only option that does not describe a rigid motion transformation is:
A. dilating a figure by a scale factor of [tex]\(\frac{1}{4}\)[/tex].
