IXL - Dilations: find the scale factor and center of the dilation (Geometry practice)

In the graph below, trapezoid

is the image of

after a dilation.

What are the scale factor and center of the dilation?

Simplify your answers and write them as fractions or whole numbers.

scale factor:

center of the dilation:

)

ref_doc_title.

Learn with an example

question

In the graph below, quadrilateral

is the image of

after a dilation.

What are the scale factor and center of the dilation?

Simplify your answers and write them as fractions or whole numbers.

scale factor:

center of the dilation:

)

key idea

A dilation is a transformation that enlarges or shrinks a figure proportionally around a fixed point. The fixed point is called the center of the

dilation.

The scale factor of the dilation tells you whether the dilation enlarges or shrinks, and by how much. It is equal to the ratio of a length in the image after the dilation to the corresponding length in the original figure.

solution

is the image of

after a dilation. You want to find the scale factor and center of the dilation.

Find the scale factor.

First, find

by plugging the endpoints

(

–

)

and

(

)

into the distance formula.

(

–

(

–

)

(

–

)

(

)

(

)

Now, find

by plugging the endpoints

(

–

)

and

(

)

into the distance formula.

(

–

(

–

)

(

–

)

(

)

(

)

Last, determine the scale factor by finding the ratio of

The scale factor is

Find the center of the dilation.

Each point on

, its corresponding point on

, and the center of the dilation must be collinear, since each point on

the distance from the center of the dilation to its corresponding point on

So, to find the center of the dilation, you can draw a line through

and

and another line through

and

and see where the lines intersect.

The center of the dilation is

(

–

)

Looking for more? Try these:

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:

I.4Dilations: find the scale factor

I.1Dilations: graph the image

Lesson: Dilations

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!