Question

Math

Posted 2 months ago

```
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
```

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Answer from Sia

Posted 2 months ago

Solution by Steps

step 2

A rotation about a point $P$ also preserves both angle measures and segment lengths

step 3

Another reflection over $\overleftrightarrow{PQ}$ again preserves both angle measures and segment lengths

step 4

A rotation about a point $Q$ preserves both angle measures and segment lengths

step 5

Since all transformations in the sequence preserve both angle measures and segment lengths, the overall sequence must preserve both angle measures and segment lengths

C

Key Concept

Preservation of geometric properties under transformations

Explanation

Reflections and rotations are rigid motions that preserve both angle measures and segment lengths.

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