Dilations

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. y 10 9 8 7 6 A’ 5 4 3 2 A 1 0 1 2 3 4 5 6 7 8 9 10 x 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? 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. Repeat for all the other vertices. Connect your new points to create your dilated shape.

4. y 9 8 7 6 5 4 B 3 B’ 2 1 0 1 2 3 4 5 6 7 8 9 10 x What if the center of dilation is inside the shape? Dilate shape B with scale factor 2 and with a center of dilation (6,6).

5. y 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 x What about scale factors less than 1? Dilate the quadrilateral by scale factor ½ and center of dilation (10,1). 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. y 10 9 8 7 6 5 E 4 3 2 D 1 0 1 2 3 4 5 6 7 8 9 10 x How do I find the center of dilation? Connect the corresponding vertices and extend the lines. The point where they all intersect is your center of dilation. Center = (2,9) What was the scale factor of the dilation?