To compare dilation transformations with translations, rotations, and reflections, let's analyze each option provided:
a. All transformations move figures across the coordinate plane: This is not true for all transformations. While translations do move figures, rotations and reflections change the orientation and position of figures, and dilations change the size but do not necessarily move the figures across the coordinate plane.
b. Dilation transformations make figures larger; translations shrink figures: This is incorrect. Dilation transformations can either enlarge or reduce the size of a figure depending on the scale factor applied. Translations do not change the size of figures; they simply move them without altering their dimensions.
c. All transformations change the size and shape of figures: This is also incorrect. While dilation changes the size of a figure (and can change the shape if the scale factor is not uniform), translations, rotations, and reflections only change the position or orientation of a figure without altering its size or shape.
d. Dilation transformations are the only ones that do not maintain the same side lengths: This is accurate. Dilation changes the size of the figure and, consequently, the side lengths. In contrast, translations, rotations, and reflections preserve the side lengths and shape of the figures.
Given this analysis, the most accurate statement is:
d. dilation transformations are the only ones that do not maintain the same side lengths.
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