Question

how does a dilation transformation compare to translations, rotations, and reflections? (1 point)

• dilations transformations are the only ones that do not maintain the same side lengths.
• dilations transformations make figures larger, translations shrink figures.
• all transformations move figures across the coordinate plane.
• all transformations change the size and shape of figures.

Explanation:

To determine the correct answer, we analyze each option:

• Option 1: Dilations change the size (scale) of figures, so they don't maintain side lengths. Translations, rotations, and reflections (rigid transformations) do maintain side lengths. So this is incorrect.
• Option 2: Dilations are not transformations that move figures (translations do that), and dilations change size, while translations, rotations, and reflections are rigid (preserve size/shape). So this is incorrect.
• Option 3: All transformations do not change size and shape. Dilations change size, so this is incorrect.
• The correct reasoning is about rigid transformations (translations, rotations, reflections) maintaining side lengths, while dilations (non - rigid) change size. But among the given options, the one that aligns with the properties of rigid transformations (translations, rotations, reflections) is the idea that these rigid transformations (translations, rotations, reflections) maintain side lengths, while dilations do not. Wait, re - evaluating the options: The option "All transformations move figures across the coordinate plane" is incorrect as dilations don't move figures but change size. The option "Dilation transformations make figures larger; translations shrink figures" is incorrect as translations don't shrink figures. The option "All transformations change the size and shape of figures" is incorrect as rigid transformations don't. The correct option (the one that was selected with the blue dot) is incorrect? Wait, no, let's re - read the question: "How does a dilation transformation compare to translations, rotations, and reflections?"

Dilations: change the size (scale) of the figure, do not preserve side lengths (non - rigid transformation).
Translations, rotations, reflections: do not change size or shape (rigid transformations), preserve side lengths.
So the correct statement about the comparison is that translations, rotations, and reflections (rigid transformations) maintain side lengths (and size/shape), while dilations do not. Among the options, the option that was marked (the first option) says "Dilation transformations are the only ones that do not maintain the same side lengths" which is correct because translations, rotations, and reflections (rigid transformations) do maintain side lengths, and dilations (non - rigid) do not. So that option is correct.

Answer:

The option with the blue dot (the first option: "Dilation transformations are the only ones that do not maintain the same side lengths")