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.

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

Scale factor 1/3 O O’ F’ R’ F R

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

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.

Dilations Example 1:

Dilations

Dilations

Dilations

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

(-2,0) (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 _________________