Question

Circle A ′ A ′ , prime is the result of reflecting circle A AA across the line ℓ ℓ.

Select all of the correct statements about the unchanged properties of circle A AA and circle A ′ A ′ , prime.

A) The radii of circle A AA and circle A ′ A ′ , prime have the same lengths.
B) Circle A AA and circle A ′ A ′ , prime have the same circumference.
C) Circle A AA and circle A ′ A ′ , prime have the same area.
D) None of the above

Answer 1

When Circle A is reflected across a line to become Circle A', properties like the radii lengths, circumference, and area remain unchanged. Options A through C are correct, as they refer to these invariant characteristics after reflection.

Step-by-step explanation:

The question asks about the properties that remain unchanged when a circle, Circle A, is reflected across a line to become Circle A'. Reflection is a transformation that creates a mirror image of a shape across a line, but it does not change the size or shape of the figure. Hence, the following properties remain unchanged:

• The radii of Circle A and Circle A' have the same lengths because a reflection does not alter lengths.
• Circle A and Circle A' have the same circumference, as the circumference is calculated using the radius, which remains unchanged.
• Circle A and Circle A' have the same area, calculated with the radius as well, and since the radius does not change, neither does the area.

Therefore, all the options (A through C) are correct as they represent properties that remain the same after Circle A is reflected across line ℓ to become Circle A'.