Notes Dilations

DefinitionsDilation - a transformation in which every point P

has an image P' placed on OP so that

and OP' = k * OP

Center of Dilation – the point from which an original figure is dilated.

Scale Factor - the ratio of the image length to the corresponding original length.

'OPk

OP

Scale Factor• If the scaled factor is greater than 1, then it

is an enlargement (k>1).

• If the scaled factor is equal to 1, then it is a congruent figure (k=1)

• If the scale factor is less than 1, then it is a reduction (k<1).

Corresponding distances

42

= = 2Image Distance

Original Distance= k

Scale Factor

2 > 1

This dilation is an enlargement .

Corresponding distances

23

= Image Distance

Original Distance= k

Scale Factor

2/3 < 1

This dilation is an reduction.

Example:1. Rectangle W’X’Y’Z’

is the image of rectangle WXYZ after a dilation.

a. Find the scale factor of the dilation.

b. Tell whether the image is a reduction or an enlargement.

Example:2.

Example:3.

Reduction, Enlargement, or Congruent?

1. K = 4

2. K = ½

3. K = 1

4>1 Enlargement

½ <1 Reduction

Congruent

MatchingA. K = ¼

B. K = 3

C. K = 2/7

D. K = 1

E. K = 5

F. K = 3/8

Reduction

Enlargement

Congruent

7. scale factor 2

8. scale factor ¼

8. scale factor 1/3