IXL - Similarity of circles (Geometry practice)

You can transform circle

to circle

by translating it and then performing a dilation centered at

Find the translation rule and the scale factor of the dilation.

Simplify the scale factor and write it as a proper fraction, improper fraction, or whole number.

Translation:

(

)

↦

Scale factor:

ref_doc_title.

Learn with an example

question

You can transform circle

to circle

by translating it and then performing a dilation centered at

Find the translation rule and the scale factor of the dilation.

Simplify the scale factor and write it as a proper fraction, improper fraction, or whole number.

Translation:

(

)

↦

Scale factor:

key idea

The image of the point

(

)

translated

units horizontally and

units vertically is

(

)

is positive the point is translated to the right and if

is negative the point is translated to the left. If

is positive the point is translated up and if

is negative the point is translated down.

Dilating a circle about its center multiplies its radius by the scale factor of the dilation.

solution

Performing a translation and dilation can transform a circle into any other circle. In other words, all circles are similar.

Circle

is a translation and dilation of circle

First, find the translation that maps the center of circle

to the center of circle

The difference in the

-coordinates

(

–

)

and

(

–

)

–

The difference in the

-coordinates

(

–

)

and

(

–

)

–

(

–

)

So, if you shift

(

–

)

9 units to the left and 7 units up, you arrive at

(

–

)

In other words, the translation that maps

(

–

)

(

–

)

is given by the rule

(

)

↦

(

–

)

After translating the center of circle

to the center of circle

dilate circle

about its new center to shrink circle

onto circle

To find the scale factor of this dilation, calculate the ratio of the radii. Notice that the radius of circle

is 2 and the radius of circle

is 8. Since you are shrinking circle

onto circle

the dilation scale factor is the ratio of 2 to 8, which is

In summary, the translation and scale factor are:

Translation:
(
x
,
y
)
↦
(
x
–
9
,
y
+
7
)
Scale factor:
1
4

Looking for more? Try these:

Lesson: Translations

Lesson: Dilations

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	06

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

H.4Translations: write the rule

I.4Dilations: find the scale factor

M.1Ratios in similar figures

Lesson: Translations

Lesson: Dilations

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!