UNIT 5Similarity

Dilation A dilation is a transformation that maps every point in a pre-image to another pointin an image by enlarging or reducing by aspecific scale factor with center C.

Scale Factor The constant term that determines the sizeof the dilation.

Represented by the letter k

Notation DCenter, k

Example

D(o,o), 2 means a dilation from the Origin (0,0), with a scale factor of 2

Reduction Makes the pre-image smaller. When k is between 0 and 1.

0 < k < 1

Enlargement Makes the pre-image larger. When k is greater than 1

A

B

C

B’

A’

F’

A’A

B

B’F’

F

C

F

Scale Factor k =

k =

A

B

B’

A’

F’

C

F

5

10

Properties of Dilation A dilation is NOT an isometric transformation. It preserves shape,

but not size.

Angle Measures stay the same.

Things that were parallel are still parallel.

Points that were on a line remain on that

line.

Orientation remains the same.

Distance is NOT preserved.