9.5 Dilations Dilation: a transformation that produces an image that is the same shape as the original, but is a different size. A dilation stretches or shrinks the original 9igure. •  Dilations are generally not an isometry (rigid motion)
•  Dilations produce similar 9igures
Properties preserved under a dilation… 1. 
2. 
3. 
4. 
5. 
angle measures parallelism colinearity midpoint orienta8on Properties NOT preserved under a dilation… 1. distance Scale Factor: measures how much larger or smaller an image is
•  A scale factor > 1 is an enlargement.
•  A scale factor between 0 and 1 is a reduction. The center of dilation is a 9ixed point in the plane about which all points are expanded or contracted. It is the only point that does not move!
Graph the image of the 9igure using the transformation give.
Example 1: Draw the dilation image of triangle CNP with the center of dilation at the origin and a scale factor of 2. •  To dilate an image with the origin as its center, simply multiply each coordinate by its scale factor
Example 2: Draw the dilation image of triangle BMN with the 1
center of dilation at the origin and a scale factor of 2 . Example 3: The blue triangle is a dilation image of the red triangle. Describe the dilation. Example 4: Quadrilateral PQRS has vertices P (-­‐2, 4), Q (4, 4), R (4, -­‐2), and S (-­‐ 4, -­‐ 4). It is dilated by a scale factor of ½. a) What are the coordinates of the image? Graph them. b) Demonstrate these quadrilaterals are similar by comparing the ratios of the lengths. c) What do you notice about the angle measurements of the two 9igures?
Example 1: Dilate the point (6, -­‐2) by a scale factor of ½ using a center of dilation of (2,4)
1)  Find the slope between the two points. (Go from the center of dilation to the point given.) 2)  Multiply the numerator AND the denominator of the slope by the scale factor. 3)  Use your new slope from step 2 to plot your new point. Start at the center of dilation. In this case, you would go down 3, right 2. Example 2:
•  Since we’re doubling the distance vertically, we now need to go up ______________.
This is the same as ____________________ to the ____ coordinate. •  Since, we’re also doubling the distance horizontally, we need to go right
____________. This is the same as __________________ to the _____ coordinate. Example 3: •  From the center of dilation, we need to go _______________________________________. This is the same as _____________________ to the y-­‐coordinate, and ______________________________ the x-­‐coordinate. The center of dilation, pre-image
point, and image point will all be
COLINEAR.