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

Amias can dilate circle A by a factor of ab 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 upper A by a factor of Start Fraction a over b End Fraction and show that the circles now coincide. Because a sequence of transformations maps circle upper A onto circle upper B , circle upper A is similar to circle upper 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 both circle upper A and circle upper B around their center points until they coincide. Because a sequence of transformations maps circle upper A onto circle upper B , circle upper A is similar to circle upper B .

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

Answer 1

To complete Amias's proof that any two given circles are similar, he can dilate circle A by a factor of \( \frac{b}{a} \) (the ratio of the radii of circle B to circle A) to show that the circles now coincide. Since dilation is a transformation that preserves the shape, Amias can conclude that circle A is similar to circle B.

So the correct response is:

Amias can dilate circle A by a factor of \( \frac{b}{a} \) 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.