Question

select all of the correct statements about the unchanged properties of circle a and circle a

choose all answers that apply:

a points a and a have the same coordinates.
b circle a and circle a have the same area.
c the radii of circle a and circle a have the same lengths.
d none of the above

Explanation:

Step1: Analyze Option A

If there is a transformation (not shown in the problem but implied by the notation \(A\) and \(A'\)), the coordinates of \(A\) and \(A'\) are likely to change (unless it's a transformation that maps a point to itself, but no information is given to suggest that). So, Option A is incorrect.

Step2: Analyze Option B and C

When a circle is transformed (assuming it's a rigid - motion transformation like translation, rotation, or reflection), the radius of the circle remains the same. The area of a circle is given by the formula \(A=\pi r^{2}\), and if \(r\) (radius) is unchanged, then the area is unchanged. Also, since the radius length \(r\) is a property of the circle, if the transformation is a rigid motion (which preserves distances), the length of the radius of circle \(A\) and circle \(A'\) is the same.

Answer:

B. Circle \(A\) and circle \(A'\) have the same area.
C. The radii of circle \(A\) and circle \(A'\) have the same lengths.