Question

what is true of a sequence of transformations that rotates an image and then translates it in order to map it onto another image? select all that apply. it includes exactly two rigid - transformations. distance is preserved. it includes only one rigid transformation. it results in figures that have the same shape but different sizes. it preserves angle measures.

Explanation:

Step1: Recall rigid - transformation properties

Rigid transformations include rotations, translations, and reflections. A sequence of a rotation and a translation is a composition of two rigid - transformations. Rigid transformations preserve distance and angle measures. They result in congruent figures (same shape and same size).

Step2: Analyze each option

• Option 1: A rotation and a translation are two rigid - transformations, so "It includes exactly two rigid transformations" is true.
• Option 2: Rigid transformations preserve distance, so "Distance is preserved" is true.
• Option 3: It includes two rigid transformations (rotation and translation), not one, so "It includes only one rigid transformation" is false.
• Option 4: Rigid transformations result in congruent figures (same shape and same size), not just same - shape different - size, so "It results in figures that have the same shape but different sizes" is false.
• Option 5: Rigid transformations preserve angle measures, so "It preserves angle measures" is true.

Answer:

It includes exactly two rigid transformations, Distance is preserved, It preserves angle measures.