Amias is trying to prove that any two given circles are similar. He starts by drawing circle A with a radius of a and circle B with a radius of b where a≠b. He then translates circle A so that circle A and circle B have the same center. How can he complete his proof to show that circle A is similar to circle B?(1 point)

Question

Responses
Amias can dilate circle A by a factor of a/b and show that the circles now coincide. Because a sequence of transformations maps circle A onto circle B, circle A is similar to circle B.
Amias can dilate circle A by a factor of b/a and show that the circles now coincide. Because a sequence of transformations maps circle A onto circle B, circle A is similar to circle B.

Amias can rotate both circle A and circle B around their center points until they coincide. Because a sequence of transformations maps circle A onto circle B, circle A is similar to circle B.

Amias can rotate circle A around its center point until it coincides with circle B. Because a sequence of transformations maps circle A onto circle B, circle A is similar to circle B.

Answer 1

The correct response is:

Amias can dilate circle A by a factor of b/a and show that the circles now coincide. Because a sequence of transformations maps circle A onto circle B, circle A is similar to circle B.

This is because dilation is a geometric transformation that preserves the shape of the figure. Since similarity is defined by whether one shape can be transformed into another via scaling (dilation), translation, and rotation, Amias's dilation of circle A to match circle B demonstrates their similarity.