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)

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 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 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 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
.

Answer 1

Choose the dilation by factor b/a.

Reason: After translating the centers to coincide, dilating circle A by factor b/a multiplies its radius a by b/a to get radius b, so the two circles coincide. A translation followed by a dilation (a composition of similarity transformations) maps A to B, so the circles are similar.