Question

a sequence of transformations is described below: - a reflection over a line \\(\overleftrightarrow{pq}\\) - a rotation about the point \\(p\\) - a translation which of the following must be preserved under this sequence of transformations? choose 1 answer: a angle measures only b segment lengths only c both angle measures and segment lengths d neither angle measures nor segment lengths

Explanation:

Step1: Recall Transformations' Properties

Reflection, rotation, and translation are all rigid transformations. Rigid transformations preserve both angle measures and segment lengths (they preserve the shape and size of the figure, only changing its position or orientation).

Step2: Analyze Each Transformation

• Reflection: Preserves angle measures and segment lengths.
• Rotation: Preserves angle measures and segment lengths.
• Translation: Preserves angle measures and segment lengths.

Since all three transformations in the sequence are rigid, both angle measures and segment lengths are preserved.

Answer:

C. Both angle measures and segment lengths