Dilations Objective:

A Dilation can enlarge or reduce a figure by a scale factor. What is a Dilation? A dilation is a transformation that changes the size but not the shape of the figure. We use “  ” to identify new points.

Scale Factor What is a Scale Factor? A scale factor is scale that enlarges or reduces similar figures, can be expressed as a decimal, a fraction, or percent. Example: A 10% increase is a scale factor of 1.1 and a 10% decrease is a scale factor of 0.9.

Helpful Hints!! A scale factor between 0 and 1 reduces a figure. A scale factor greater than 1 enlarges it. Scale Factor = 2 Scale Factor = 1/2

Try This!!! The transformation is a dilation Tell whether each transformation is a dilation. The transformation is a dilation The transformation is not a dilation

Try This!!! The transformation is a dilation Tell whether each transformation is a dilation. B A C A' B' C' A' B' C' A B C The transformation is not a dilation. The figure is changed. The transformation is a dilation

Center of Dilation What is the center of Dilation? A center of dilation is a fixed point of every dilation, found by drawing a line that connects each of the pairs of corresponding vertices.

P and P’ are the same point Try This!!! Dilate the figure by a scale factor of 0.4 with P as the center of dilation. Multiply each side by 0.4 P and P’ are the same point

Try This!!! Dilate the figure by a scale factor of 1.5. What are the vertices of the image? Multiply the coordinates by 1.5 to find the vertices of the image The vertices of the image are

Try This!!! Dilate the figure by a scale factor of . What are the vertices of the image? Multiply the coordinates by to find the vertices of the image The vertices of the image are

Example 1:

Example 2:

Example 3: Dilate the figure by a scale factor of 2. What are the vertices of the image? 2 4 6 8 10 B C A

Example 4: Dilate the figure by a scale factor of 0.5. What are the vertices of the image? 2 4 6 8 10 B C A