Question

page 7 of 7 Similar Circles Quick Check 3 of 53 of 5 Items Question 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) Responses 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 . 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 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 . Skip to navigation

Answer 1

To complete his proof that circle A is similar to circle B, Amias needs to demonstrate that one circle can be transformed into the other through a series of transformations, specifically a dilation.

The best option among the provided responses 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.**

This is correct because dilating circle A by a factor of \( \frac{b}{a} \) will proportionally increase or decrease its radius to match the radius of circle B, thus proving that the two circles are similar.