Dilations

Learning Target: I can use a scale factor to make a larger or smaller copy of a figure that is also similar to the original figure.

A dilation with center of dilation C and scale factor n can be written as D(n,c). A dilation is a transformation with the following properties.·The image of C is itself (C'=C)·For any other point R, R' is on CR and CR'=n*CR, or n=CR'·Dilations preserve angle measure.

CR___

P

Q

R

P'

Q'

R'

C'=C

CR'=n*CR

P

Q

R

P'

Q'

R'

C'=C

CR'=n*CR

The scale factor n of a dilation is the ratio of a length of the image to the corresponding length in the preimage, with the image length always to the numerator.

n =CR'

CR

R'P'

RP

P'Q'

PQ

Q'R'

QR

__ ___ ___ ___= = =

A dilation is an enlargement if the scale factor n is greater than 1. The dilation is a reduction if the scale factor n is between 0 and 1.

C

D

2

4

C'

D'

B'

B

A'=A

2

8

F

E

G

H

E'

F'

H'

G'

C

Enlargementcenter A, scale factor 2

Reductioncenter C, scale factor 1/4