Dilations A dilation is a transformation that changes

Dilations A dilation is a transformation that changes the size but not the shape of an object or figure. Every dilation has a fixed point that is called the center of dilation.

Dilations: (Stretching/Shrinking) • Dilations use a scale factor to reduce or enlarge shapes. • Every dilation has a center and a scale factor. Most of the time it is the origin (0, 0) • Scale Factor: tells you how many times larger or smaller your image will be. • The new shape and the image are similar. Dilations are also called similarity transformations.

• scale factor of 2 • center of dilation at the origin. C’ B’ B A A’ C D D’

• Scale factor 1/3 O O’ F’ F R’ R

Example 3: • Scale factor 4 T T’ S S’ H H’ I I’

• The dilation is an enlargement if the scale factor is > 1. • The dilation is a reduction if the scale factor is between 0 and 1.

Dilations To dilate an object: 1) Graph object if necessary. 2) Multiply the coordinates of the object by the scale factor. 3) Graph new coordinates.

Example 1: Dilations

Dilations

Dilations

Dilations

(0, 2) (0, 0) Dilate by a scale factor of 2 (3, 0)

(-2, 0) (-2, -1) (2, -1) Dilate by a scale factor of 3

Dilate by a scale factor of ½

Closure • How is a dilation different from our other transformations?

Closure • When the scale factor is greater than 1, does the shape get larger or smaller?

Closure • If the scale factor is less than one, the shape gets _________