Question

Question
1
Question
2
A)
You can prove that two circles are similar to each other because the ratio of radius to radius takenanywhere within two circles is uniform. What is the process of growing or shrinking a circle from one tothe other called?
(1 point)
reflection
rotation
dilation
translation
A)
Dilations are transformations that produce similar figures; therefore, all circles are
(1 point)
similar.
congruent.
concentric.
parallel.
Question
3
Question
4
A)
Amias is trying to prove that any two given circles are similar. He starts by drawing circle
with aradius of
a
and circle
with a radius of
b
where
. He then translates circle
so that circle
andcircle
have the same center. How can he complete his proof to show that circle
is similar to circle
?
(1 point)
A
B a ≠ b A A
B A
B
Amias can rotate circle
around its center point until it coincides with circle
. Because a sequence oftransformations maps circle
onto circle
, circle
is similar to circle
.
A
B
A
B
A
B
Amias can dilate circle
by a factor of
and show that the circles now coincide. Because a sequence oftransformations maps circle
onto circle
, circle
is similar to circle
.
A
b
a
A
B
A
B
Amias can dilate circle
by a factor of
and show that the circles now coincide. Because a sequence oftransformations maps circle
onto circle
, circle
is similar to circle
.
A
a
b
A
B
A
B
Amias can rotate both circle
and circle
around their center points until they coincide. Because asequence of transformations maps circle
onto circle
, circle
is similar to circle
.
A
B
A
B
A
B
A)
If the circumference of circle
X
is
and the circumference of circle
Z
is
, then what is the scalefactor from
X
to
Z
?
(1 point)
12π 6π
2
:
1
1
:
3
3
:
1
1
:
2
Question
5
A)
If the radius of circle
is 14 meters and it is dilated by a scale factor of 2.5, then what will be thecircumference of circle
?
(1 point)
O
O′
345 m
10 m
44 m
220 m

Answer 1

Q1: dilation.
(You grow or shrink a circle by a dilation.)

Q2: similar.
(All circles are similar.)

Q3 (proof): Dilate the circle of radius a by a factor of b/a so its radius becomes b; then the two circles coincide, so they are similar.

Q4: 1 : 2.
(Scale factor from X (12π) to Z (6π) is 6π/12π = 1/2.)

Q5: 220 m.
(New radius = 14 × 2.5 = 35 m; circumference = 2π·35 = 70π ≈ 220 m.)