9.5 Dilations

9.5 Dilations

9.5 DilationsBrett Solberg AHS 11-12Warm-upDraw all the lines of symmetry. What is the angle of rotation?

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Todays AgendaWarm-up/HW Review

Chapter 9 Review

9.5 DilationsScale Factorenlargement reduction

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Homework Worksheet Packet9.2 Graphing PacketReview Worksheet

TransformationsTranslations (slide)rule of (4, -5)

Reflections (flip)x-axis(x, y) (x, -y)y-axis(x, y) (-x, y)line

RotationsCenter of Rotationprotractorcompass

Rotating about Origin90 clockwise (x, y) (y, -x)90 counterclockwise (x, y) (-y, x)180 either way (x, y) (-x, -y)

RotationRotate 90, 180, 270

SymmetryReflection Symmetrylines of symmetry

Rotational Symmetryangle of rotation

DilationA dilation is a transformation whose image and preimage are similar.

DilationEyes Dilating

Scale Models

VocabularyScale Factor determines the size change from the original figure to its image.

The dilation is an if the scale factor is greater than 1.

The dilation is a if the scale factor is between 0 and 1. enlargementreductionExample 1Find the scale factor. The red square is the dilation of the blue square. 2244Example 3Scale Factor = 2

Example 2PointScale FactorImage(2, 3)3(6, 2)(-2, 0) 2(4, -1)1/3 (10, 15)20(-10, -20) 1/5Built in 1974, originally called the Sears tower.

Stands at 1451ft (442m)

Was the worlds tallest building for 25 years

Currently the tallest building in USA.Willis Tower

15The ratio of height to width is 6.45:1.

The building is 1451 ft tall. What is the width?Willis Tower

16Willis Tower LEGO Model (Sears Tower)

scale model

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Willis Tower Scale Model18The ratio of height to width is 6.45:1 If the width of the model is 3 ft, and the model is similar to the actual tower, how tall is the model?Solving Proportions

19Jaguar ProportionActual Dimensionswidth 75 incheslength 189 inches

Model dimensionswidth 7 incheslength 20 inches

Does a dilation occur?

AssignmentsAssignmentsWorksheet Packet (50 points)9.2 Graphing Packet (10 points)Review Worksheet (10 Points)Warm-ups (10 points)Extra Credit Opportunitiespg 523 #1 - 29 Postertranslationreflectionrotationdilation