Question

how are dilations of polygons using a scale factor not equal to 1 different from translations, reflections, or rotations of polygons? (1 point) they produce an image that is congruent to the preimage. they do not preserve angle measures of corresponding vertices. they do not preserve shape. they do not preserve distance between corresponding vertices.

Explanation:

1. Recall the properties of transformations:

• Translations, reflections, and rotations are rigid transformations. Rigid transformations preserve distance (so corresponding sides are equal) and angle measures, and produce congruent figures (same shape and size).
• Dilations are non - rigid transformations. A dilation with a scale factor \(k

eq1\) changes the size of the figure.

• For a dilation, the shape of the figure is preserved (it is similar), angle measures are preserved, but the distance between corresponding vertices (side lengths) is multiplied by the scale factor \(k\). So, if \(k

eq1\), the distance between corresponding vertices is not preserved.

• Option 1: Dilations with \(k

eq1\) do not produce congruent figures (since size changes), so this is incorrect.

• Option 2: Dilations preserve angle measures, so this is incorrect.
• Option 3: Dilations preserve the shape (the figure remains similar), so this is incorrect.
• Option 4: Since dilation changes the size (multiplies side lengths by the scale factor), the distance between corresponding vertices is not preserved, which is different from rigid transformations (translations, reflections, rotations) that do preserve distance.

Answer:

D. They do not preserve distance between corresponding vertices.