You can prove that two circles are similar to each other because the ratio of radius to radius taken anywhere within two circles is uniform. What is the process of growing or shrinking a circle from one to the other called? (1 point)

Question

• rotation
• reflection
• dilation
• translationDilations are transformations that produce similar figures; therefore, all circles are (1 point)
• concentric.
• congruent.
• similar.
• parallel.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)
Amias can dilate circle A by a factor of a and show that the O circles now 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.
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 dilate circle A by a factor off 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.

Answer 1

1. The process of growing or shrinking a circle from one to the other is called dilation.

2. Therefore, all circles are similar.

3. To complete his proof to show that circle A is similar to circle B, Amias can dilate circle A by a factor of \(\frac{b}{a}\) (not "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.

(Note: If "a" was intended instead of "b" in the last option, it would be an error. The correct factor for dilation should involve the ratio of the radii, typically expressed as \(\frac{b}{a}\)).

So the final options would align closer to: 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.