Dilations Learning Target: I can use a scale factor to make a larger or smaller copy of a figure that is also similar to the original figure.

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Dilations Learning Target: I can use a scale factor to make a larger or smaller copy of a figure that is also similar to the original figure.

A dilation with center of dilation C and scale factor n can be written as D (n,c). A dilation is a transformation with the following properties. ·The image of C is itself (C ' =C) ·For any other point R, R' is on CR and CR'=n*CR, or n=CR' ·Dilations preserve angle measure. CR ___ P Q R P' Q' R' C'=C CR'=n*CR

P Q R P' Q' R' C'=C CR'=n*CR The scale factor n of a dilation is the ratio of a length of the image to the corresponding length in the preimage, with the image length always to the numerator. n = CR' CR R'P' RP P'Q' PQ Q'R' QR __ ___ = ==

A dilation is an enlargement if the scale factor n is greater than 1. The dilation is a reduction if the scale factor n is between 0 and 1. C D 2 4 C' D' B' B A'=A 2 8 F E G H E' F' H' G' C Enlargement center A, scale factor 2 Reduction center C, scale factor 1/4