A dilation transformation differs from translations, rotations, and reflections in several key ways:
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Change in Size: Dilation transformations change the size of figures—either enlarging or shrinking them—while maintaining their shape (the proportions of the figure). In contrast, translations, rotations, and reflections do not alter the size or shape; they only change the position or orientation of the figure.
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Maintaining Side Lengths: Dilation transformations do not maintain the same side lengths of the figures—either the lengths increase or decrease depending on the dilation factor. In contrast, translations, rotations, and reflections preserve the side lengths, keeping the figures congruent to their originals.
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Types of Movement: Translations, rotations, and reflections all involve moving figures across the coordinate plane in specific ways (sliding, rotating about a point, or flipping over a line, respectively). Dilation, on the other hand, involves resizing figures around a center point, which may or may not be the same as the center of rotation or reflection.
In summary, dilation transformations are unique in that they alter the size of figures while retaining their shape, while the other transformations (translations, rotations, reflections) maintain both size and shape but change the figures' position or orientation.