Question

11
which of these properties of a rigid transformation is exclusive to translations?
a. the measures of the angles and sides in the preimage are preserved.
b. the points in the preimage lie in the same plane as the points in the image.
c. all the points in the preimage are shifted the same distance.
d. the orientation of sequences of points in the preimage are always preserved.
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Explanation:

• Option A: Preservation of angles and side - lengths is a property of all rigid transformations (translations, rotations, reflections), not just translations.
• Option B: All rigid transformations (since they are planar transformations) have the property that the pre - image and image lie in the same plane.
• Option C: In a translation, every point of the pre - image is moved (shifted) the same distance in the same direction. Rotations and reflections do not have this property. For a rotation, points move along circular paths with different distances from the center of rotation, and for a reflection, points are "flipped" over a line (not shifted the same distance in a uniform direction).
• Option D: The orientation of sequences of points is preserved in translations and rotations but is reversed in reflections.

Answer:

C. All the points in the preimage are shifted the same distance.