1. Dilations Objectives:
To be able to dilate shapes given a scale factor and centers of dilation.
Find centers of dilation.

2. Scale factors and Centers of Dilation
The size of a dilation is described by its scale factor.
For example, a scale factor of 2 means that the new shape is twice the size of the original.
The position of the image depends on the location of the center of dilation.

3. A’ How do I dilate a shape? y 10 9 8 7 6 5 4 3 A 2 1
Dilate triangle A with a scale factor of 3 and center of dilation (2,1).
Draw lines from the center of the dilation to each vertex of your shape.
How do I dilate a shape? x 1 9 8 7 6 5 4 3 2 y 10
Calculate the distance from the center of the dilation to a vertex of the preimage and multiply it by the scale factor to find the distance the image point is from the center. A’
Repeat for all the other vertices. A
Connect your new points to create your dilated shape.

4. What if the center of dilation is inside the shape?x 1 9 8 7 6 5 4 3 2 y
What if the center of dilation is inside the shape? B’
Dilate shape B with scale factor 2 and with a center of dilation (6,6). B

5. What about scale factors less than 1?
Dilate the quadrilateral by scale factor ½ and center of dilation (10,1). x 1 9 8 7 6 5 4 3 2 y
Each vertex on the dilated shape is half the distance from the center than its corresponding vertex on the original shape.
Even though the shape gets smaller, it’s still called a dilation.

6. How do I find the center of dilation?x 1 9 8 7 6 5 4 3 2 y 10
Connect the corresponding vertices and extend the lines.
The point where they all intersect is your center of dilation. E
Scale factor could be 2 or ½ depending on which way they enlarge the shapes D
Center = (2,9)
What was the scale factor of the dilation?