A sequence of transformations is described below.
- A reflection over a line $\overleftrightarrow{P Q}$
- A rotation about the point $P$
- Another reflection over $\overleftrightarrow{P Q}$
- A rotation about the point $Q$

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

Question

A sequence of transformations is described below.
- A reflection over a line $\overleftrightarrow{P Q}$
- A rotation about the point $P$
- Another reflection over $\overleftrightarrow{P Q}$
- A rotation about the point $Q$

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

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the transformations given in the sequence and their properties. ‖ ‖ step 2 ⋮ A reflection over a line preserves angle measures and segment lengths. ‖ ‖ step 3 ⋮ A rotation about a point preserves angle measures and segment lengths. ‖ ‖ step 4 ⋮ The sequence includes two reflections over the same line and two rotations about points, which are all isometries. ‖ ‖ step 5 ⋮ Since all transformations in the sequence are isometries, they preserve both angle measures and segment lengths throughout the sequence. ‖ ∻Answer∻ ⚹ (C) Both angle measures and segment lengths ⚹ ∻Key Concept∻ ⚹Isometries in Geometry⚹ ∻Explanation∻ ⚹Reflections and rotations are isometries, which means they preserve distances and angles. Therefore, a sequence of these transformations will preserve both angle measures and segment lengths.⚹◊What mathematical properties are preserved under a sequence of transformations involving reflections and rotations?⍭ Generate me a similar question◊

Sia