Question

select all of the correct statements about the unchanged properties of circle a and circle a.
choose all answers that apply:
points a and a have the same coordinates.
circle a and circle a have the same area.
the radii of circle a and circle a have the same lengths.
none of the above

Explanation:

Step1: Analyze option A

When a circle is transformed (assuming a non - identity transformation like translation, rotation etc.), the center coordinates (points \(A\) and \(A'\)) are not necessarily the same. For example, if the circle is translated, the center moves.

Step2: Analyze option B

The area of a circle is given by the formula \(A=\pi r^{2}\). If the radius \(r\) changes (which is not stated to be the case here, but also not guaranteed to be the same in a general transformation), the area changes. In a non - scaling transformation (if it's a rotation or translation), the radius remains the same. But if it's a dilation (a type of transformation not indicated here), the radius changes. Since we don't know the transformation type, we can't assume the area is the same.

Step3: Analyze option C

The radius of a circle: similar to the area, in a non - scaling transformation (rotation, translation) the radius is the same. But if it's a dilation (a transformation that is a possibility in the absence of specific information), the radius changes. Since we don't know the transformation type, we can't assume the radius is the same.

Answer:

D. None of the above