Unformatted text preview: 8.7 Dilations 8.7
Pg 506 Dilation Dilation
• Dilation- a transformation where an Dilationobject (preimage) is enlarged or reduced (image). reduced • The image will always be marked The with primes, such as A’. with Reduction If CP=10 Reduction and CP’=5, k=? Scale factor= k
51 CP ' k= = k= 10 2 CP P preimage Reduction: 0<k<1 0<k<1 center Q’ C P’ Image Q R’ R Enlargement Enlargement
Scale factor=k k>1
CP ' k= CP P’ If CP=12 and CP’=36, and k=? k=? P Preimage 36 k= =3 12 Image C R Q Q’ R’ Center Stuff to know Stuff
• In dilations, the image and preimage In are similar figures. are • So, since Δ PQR~ Δ P’Q’R’, So, P ' Q ' = scale factor scale
PQ ** notice, the primes are on top! Ex: Identify the dilation and calculate the scale factor. the
P 3 P’ 4 C reduction CP ' 4 = CP 7 Example: Example (a.) Draw a dilation of Δ ABC w/ A(-2,1), B(-6,0), and C(-1,-1). Use the origin as the center and use a scale factor of 3/2. scale (b.) Is this an enlargement or (b.) reduction? (c.) How does the perimeter of the preimage compare to the perimeter of the image? of (a.) To get the image points, multiply each given point by the scale factor. scale
Preimage Multiply by 3/2 A(-2,1) A’(-3,3/2) B(-6,0) B’(-9,0) C(-1,-1) C’(-3/2,-3/2) B’ .
B A’ A . Image C C’ . 6 4 2 (b.) Is this an (b.) enlargement or reduction? reduction?
5 -5 -2 -4 Enlargement, Enlargement, because the scale factor is > 1. factor -6 (c.) So, how does the perimeter of does the preimage compare to the perimeter of the image? perimeter
• Since the ratio of the perimeters is Since the same as the scale factor, the ratio of the perimeters is 3/2. ratio Assignment Assignment ...
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- Spring '11
- Ratio, Scaling, Scale factor, Enlargement Enlargement