Dilation (Cartesian)Dilation (Cartesian)GraphingGraphingClassifyingClassifying

Irma Crespo 2010

Raymond’s Warm UpRaymond’s Warm Up• A man copies a picture to a certain size but does not A man copies a picture to a certain size but does not

know how big he made it. know how big he made it. Get the scale factor Get the scale factor of the of the picture to find how big the picture was made.picture to find how big the picture was made.

original

6

8

a)5b)8c) 6d)7

Author: Raymond Morrow April 2010

copy

36

48

Devin’s Warm UpDevin’s Warm Up• There are two geckos: a mom and a baby. It takes two There are two geckos: a mom and a baby. It takes two

years for a baby gecko to grow the size of its mom. If the years for a baby gecko to grow the size of its mom. If the baby gecko is half the size of its 10 inches by 2 inches baby gecko is half the size of its 10 inches by 2 inches mom, what is the size of the baby?mom, what is the size of the baby?

10 inches

2 in

ches

moma) 5 in by 2 in b) 20 in by 4 inc) 5 in by 4 ind) 5 in by 1 in

baby

Author: Devin Seamans April 2010

DilationDilation•Dilation is enlarging or Dilation is enlarging or

reducing a figure by a scale reducing a figure by a scale factor.factor.

Draw a DilationDraw a Dilation

A D

CB

Scale Factor: 2 Center Point: A

Enlargement of Polygon ABCD

D’

C’

B’

Ordered Pairs in DilationOrdered Pairs in Dilation

Scale Factor: 2

(0,0) (2,0)

(2,2)(0,1)

OriginalOriginal Multiply by Multiply by 22 ImageImage

D(2,0)

C(2,2)B(0,1)

A(0,0) A(0*2,0*2)B(0 *2,1 *2)

C(2 *2,2 *2)

D(2 *2,0 *2) D’(4,0)

C’(4,4)

B’(0,2)A(0,0)

(0,2)

(4,4)

(4,0)

ABCD AB’C’D’

On the Graphing BoardOn the Graphing Board• Plot triangle JKL Plot triangle JKL

with the following with the following ordered pairs ordered pairs (x, y)(x, y)::

• J(3,8)J(3,8)• K(10,6)K(10,6)• L(8,2)L(8,2)

• Plot triangle J’K’L’ with Plot triangle J’K’L’ with a scale factor of a scale factor of ½½ . .

JKLJKL Multiply by Multiply by ½½

J’K’L’J’K’L’

J(3,8)

K(10,6)

L(8,2) L(8* ½½,2* ½½)

K(10* ½½,6* ½½)

J(3* ½½,8* ½½)

L’(4,1)

K’(5,3)

J’(1.5,4)

On the Graphing BoardOn the Graphing Board• Plot triangle JKL Plot triangle JKL

with the following with the following ordered pairs ordered pairs (x, y)(x, y)::

• J(3,8)J(3,8)• K(10,6)K(10,6)• L(8,2)L(8,2)

• Plot triangle J’K’L’ with Plot triangle J’K’L’ with a scale factor of a scale factor of 22..

JKLJKL Multiply by Multiply by 22

J’K’L’J’K’L’

J(3,8)

K(10,6)

L(8,2) L(8* 22,2*2)

K(10* 22,6* 22)

J(3* 22,8* 22)

L’(16,4)

K’(20,12)

J’(6,16)

Find and Classify a Scale FactorFind and Classify a Scale Factor

• Quadrilateral Quadrilateral V’Z’X’W’ is a V’Z’X’W’ is a dilation of dilation of quadrilateral quadrilateral VZXW. VZXW.

V’

W’

X’Z’

Z

VX

W

COPY

ORIGINAL

Find the Scale FactorFind the Scale Factor

• Pick corresponding Pick corresponding points (ordered pairs).points (ordered pairs).

• Make a ratio of either Make a ratio of either the Xs or the Ys the Xs or the Ys following:following: V’

W’

X’Z’

Z

VX

W

coordinate point of copycoordinate point of original

V(V(-2-2,2) and V’(,2) and V’(-5-5,5),5)

V’V’VV

-5-2

OR 52

Classify the Scale FactorClassify the Scale Factor

• Scale factor isScale factor is

V’

W’

X’Z’

Z

VX

W

52

• Is it less than 1?Is it less than 1?

• Is it greater than 1?Is it greater than 1?

• It is an It is an enlargement.enlargement.

• So, it is not a reduction.So, it is not a reduction.

NO

YES

Your TurnYour TurnFind and Classify the Scale Factor (OHP)Find and Classify the Scale Factor (OHP)

B

A

A’

C

C’

B’

• Triangle Triangle A’B’C’ is A’B’C’ is a dilation a dilation of of ABC.ABC.

SummarySummary• Dilation is enlarging or reducing a figure by a scale factor.Dilation is enlarging or reducing a figure by a scale factor.

• To graph a dilation given ordered pairs and scale factor:To graph a dilation given ordered pairs and scale factor:*multiply the scale factor to each coordinate point of each ordered pair*multiply the scale factor to each coordinate point of each ordered pair*plot the scaled ordered pairs*plot the scaled ordered pairs*connect the points with line segment*connect the points with line segment

• To find the scale factor, pick corresponding ordered pairs and To find the scale factor, pick corresponding ordered pairs and create the ratio of create the ratio of

• A dilation is an enlargement if the scale factor is greater than 1.A dilation is an enlargement if the scale factor is greater than 1.

• A dilation is a reduction if the scale factor is less than 1.A dilation is a reduction if the scale factor is less than 1.

coordinate point of copycoordinate point of original

Exit SlipExit Slip• Plot line segment XY with the following ordered Plot line segment XY with the following ordered

pairs:pairs:• X(-4,2)X(-4,2)• Y(2,6)Y(2,6)

• Plot line segment X’Y’ with a scale factor of Plot line segment X’Y’ with a scale factor of ½.½. ..• Classify if the dilation is enlargement or Classify if the dilation is enlargement or

reduction. reduction. EXPLAIN!EXPLAIN! ..

Practice WorksheetPractice WorksheetComplete the practice worksheet.

Work with a partner or on your own.

Submit completed worksheet for grading.

Solutions are discussed the next day.

Skills Practice: Lesson 4-8, Page 54

Main ResourcesMain Resources• Math Connects: Concepts, Skills, and Problem

Solving; Teacher Edition; Course 3, Volume 1Columbus:McGraw-Hill, 2009.

• PowerPoint created by Irma Crespo. University of Michigan-Dearborn, School of

Education. Winter 2010.Lesson plan put together by Irma Crespo.