Teacher GuideCCS Standards

Dilation

Dim Light Normal Light

Aim: What is meant by dilation?

Do Now: Using the image below, compare the size of the lady's pupil in normal light and dim light. What characteristics stay the same and what characteristics change?

Guidemm

Drag the pupils to the ruler to compare their sizes!

Instru

ctio

ns

How do circles fit into the definition of similar triangles?

Circles?

Is each radii in the dilated pupil proportional to the corresponding radii in the dim light pupil? Proportional?

What is the definition

of similar figures? Similarity?

The shape stays the same but the size changes!

ANSWER!

Dim Light Normal Light

Dilation

is a transformation that produces an image that is the same shape as the original, but is a different size.

same shape different size

original

center

C' = C

A dilation with center of dilation C and scale factor n, n > 0, can be written as D(n, C). Properties: The image of C is itself (that is, C' = C)Dilations preserve angle measure

center of dilation scale factor

Dilation

Enlargement: a dilation used to create an image __________ than the original

Reduction: a dilation used to create an image ___________ than the original

original

center

Word Bank

n > 1

larger

smaller

n < 1

Reduction

Enlargement

n = 1

Inst

ruct

ion

sInstructions: Choose a word from the word bank and drag it into the appropriate checker box.

Scale Factor

largerlarger

Find a Dilation Image

What are the coordinates of the vertices of D2( ABC) Graph the image of ABC.

A

B

CD2(2x, 2y) Image

A(-3,4)

D2(A)=(2(-3), 2(4))

A'(-6, 8)

B(2,-2)

D2(B)=(2(2), 2(-2))

B'(4, -4)

C(4, 1)

D2(C)=(2(4), 2(1))

C'(8, 2)

-3 -2 -1 1 2 3

321

-1-2-3

x

y

Match the coordinates of the image in column B with the point in column A

D1/2(22, -8)

D3(-5, 4)

D1/4( -40, 12)

D10(15, 0)

(-15, 12)

(-10, 3)

(11, -4)

(150, 0)

Column A Column B

Determine the scale factor

A

C

-3 -2 -1 1 2 3

321

-1-2-3

A'

C'

B'

B

x

yIs Dn( ABC) = A'B'C' an enlargement or a reduction? What is the scale factor n of the dilation?

Answer: reduction, n = 1/2(press for answer)

Title Page

Attachments

Teacher Guide for dilation lesson.docx