Unit 7 Lesson 8.7: Dilations CC Standards SRT 1: Verify experimentally the properties of dilations given by a center and a scale factor. GMD 5: Know that the effect of a scale factor k greater than zero on length is to multiply by k; determine length using scale factors. Lesson goals Define and identify a dilation as an enlargement or a reduction. Use properties of dilations to solve for variables. Draw a dilation given the scale factor. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

definition Isometry A transformation that preserves lengths. Also known as a “rigid” transformation. (Figures remain congruent) Reflections, rotations and translations are all isometries.

definition Scale Factor Scale factor key vocabulary Scale Factor The ratio of the lengths of two corresponding sides for similar polygons 48 30 32 20 Scale factor

definition Dilation P I a “nonrigid” transformation that maps a preimage onto an image that is similar. P I I

definition Dilation P Reduction: the scale factor comparing the image to the preimage is between 0 and 1 P I

definition Dilation I P Enlargement: the scale factor comparing the image to the preimage is greater than 1 I P

example Determine whether the dilation from Figure A to Figure B is a reduction or an enlargement. Then, find the values of the variables. 12.5 5 x z A 3 B 3 5 y

definition Describing a Dilation I P scale factor center of dilation a fixed point in the plane about which all points are expanded or contracted. I In an enlargement, the preimage is between the center and the image. P

definition Describing a Dilation P scale factor center of dilation a fixed point in the plane about which all points are expanded or contracted. In a reduction, the image is between the center and the preimage. P I

definition I P Describing a Dilation Scale factor can be found by comparing corresponding side lengths Or by comparing the distance from the center to corresponding points Always compare the image to the preimage I P

example Find the scale factor. Tell whether the dilation is a reduction or an enlargement. C 47 in A’ B’ D’ 21.5 in A B D

example Find the scale factor. Tell whether the dilation is a reduction or an enlargement. Then find the values of the variables.

example y Draw a dilation of the figure using the given scale factor. B C B’ C’

example x y D E F G D’ 2 E’ 1 G’ F’ 1 2

summary What determines if a dilation is an enlargement or a reduction? How do you find the scale factor of a dilation? A friend asks you with help on the following problem; Draw the dilation of the figure using the given scale factor. Explain to your friend how they should solve this problem.

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