Name: _____________________________________ Date: ______________________ Period: ______
9.6 Dilations Dilation: ____________________________________________________________________________ * Requires a center point and a scale factor (r) * The value of r determines whether the dilation is an enlargement or a reduction If ! r > 1 , the dilation is an enlargement. If ! 0 < r < 1 , the dilation is a reduction. If ! r = 1 , the dilation is a congruence transformation. Similarity Transformation: ______________________________________________________________ ____________________________________________________________________________________ * Dilations are similarity transformations because they preserve angle measure, betweenness of points, and collinearity, but not distance * Theorem: If a dilation with center C and scale factor of r transforms A to B and E to D, then ! ED = r ( AB )
Examples: Find the measure of the dilation image ! A′B′ or the preimage ! AB using the given scale factor. 1. ! AB = 3 , ! r = 4
2. ! A′B′ = 8 , ! r = −
2 5
Examples: Draw the dilation image of each figure with center C and the given scale factor. 3. ! r = 4
4. ! r = −2
On the coordinate plane, you can use the scale factor to find the coordinates of the image of dilations centered at the origin. * If ! P ( x, y ) is the preimage of a dilation centered at the origin with scale factor r, then the image is ! P′ ( rx,ry ) .
Examples: 5. ! PQ has endpoint ! P ( 9,0 ) and ! Q ( 0,6 ) . Find the image of ! PQ after a dilation centered at the origin with a scale factor ! r =
1 . Sketch the preimage and image. 3
6. Triangle KLM has vertices ! K ( 5,8 ) , ! L ( −3, 4 ) , and ! M ( −1,−6 ) . Find the image of ! ΔKLM after a dilation centered a the origin with scale factor of -2. Sketch the preimage and image.
! scale factor =
image length preimage length
Examples: Determine the scale factor of each dilation with center C. Determine whether the dilation is an enlargement, reduction, or congruence transformation. 7.
8.
