Asksia AI LOGO

Sia

Question
Math
Posted 2 months ago

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

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
Sign in to unlock the answer
Answer from Sia
Posted 2 months ago
Solution by Steps
step 2
A rotation about a point P P also preserves both angle measures and segment lengths
step 3
Another reflection over PQundefined \overleftrightarrow{PQ} again preserves both angle measures and segment lengths
step 4
A rotation about a point Q 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.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages
Strong algorithms that better know you
Early access to new release features
Study Other Question