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

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.

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? 0 1 2 3 4 5 6 7 8 9 10 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.

What if the center of dilation is inside the shape? 0 1 2 3 4 5 6 7 8 9 10 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

What about scale factors less than 1? Dilate the quadrilateral by scale factor ½ and center of dilation (10,1). 0 1 2 3 4 5 6 7 8 9 10 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.

How do I find the center of dilation? 0 1 2 3 4 5 6 7 8 9 10 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?