Question

circle b is a transformation of circle a. describe the transformations that show why circle a is similar to circle b.
circle b is the result of dilating circle a with a as the center of dilation and using a scale factor of 2/3, then rotating the image 180°.
circle b is the result of dilating circle a with a as the center of dilation and using a scale factor of 2/3, then translating the image 12 units down.
circle b is the result of dilating circle a with a as the center of dilation and using a scale factor of 2/3, then reflecting the image in the y - axis.
circle b is the result of dilating circle a with a as the center of dilation and using a scale factor of 2/3, then translating the image 12 units down.

Explanation:

Step1: Analyze the position change

We can see that the center of Circle B is 12 units below the center of Circle A. There is no rotation or reflection indicated by the relative position of the circles in the coordinate - grid.

Step2: Analyze the size change

The problem states that dilation occurs first. Since the circles are similar and the position of Circle B is just a vertical shift from Circle A, and dilation is with center A. After dilation, a translation of 12 units down is needed to get from the dilated - circle to Circle B.

Answer:

Circle B is the result of dilating Circle A with A as the center of dilation and using a scale factor of $\frac{2}{3}$, then translating the image 12 units down.