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GRAB TEXTBOOKS TEAR OUT PAGES 315-319; GRAB WS AND STAPLE TOGETHER

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10.1/10.2 PROPERTIES AND ALGEBRAIC REPRESENTATIONS OF DILATIONS HOW DO YOU DESCRIBE THE PROPERTIES OF DILATIONS? Dilations change the size of figures (does not keep congruency), but NOT their orientation or shape.

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VOCABULARY OF DILATIONS ________________ changes the _____________ ( but not the _____________) of a figure. Every dilation has a fixed point called ________________________, located where the lines connecting corresponding parts of figures intersect. The center of dilation will be the _______________. The ____________________ will determine how each coordinate will either increase or decrease. Dilations size shape Center of dilation origin scale factor

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PROPERTIES OF DILATIONS An _________________ will occur when you increase the size of a figure. A _________________ will occur when you decrease the size of a figure. The ______________________ does not change. The shape will still look the same it does before. enlargement reduction orientation

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FINDING THE SCALE FACTOR Find the ratios of _____________________. 1.Identify the corresponding sides of the pre-image and the image. 2.Measure the corresponding lengths. 3.Create a ratio of the image/pre-image. The __________________ will be the length of a side on the image, and the ___________ will be the length of a side on the pre- image. corresponding side lengths numerator denominator

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PROPERTIES CONTINUED … If the dilation shows an ___________, the scale factor will be ____________ than one. If the dilation shows a reduction, the scale factor will be _____________ than one. All sides lengths must have the same scale factor for it to be a true dilation. enlargement greater less

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EXAMPLES OF ENLARGEMENTS AND REDUCTIONS Preimage _____________ Image ________________ Corresponding sides ________________ 62 Preimage _____________ Image ________________ Corresponding sides ________________ 1236 = QRSP Q’R’S’P’ QR,RS,SP,PQ ABCD A’B’C’D’ AB,BC,CD,DA

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WHAT IF YOU CAN’T MEASURE THE SIDES EXACTLY? Find the corresponding _________ of the preimage and the image and create a ratio (divide) between them. Ex: B(2, 1), B’(4,2) (______, ________) (______, ______) vertices 42 21 2 2 Scale factor of 2; Enlargement

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DILATING FIGURES ALGEBRAICALLY Multiply ALL the coordinates by the scale factor, to create the new dilation. For the scale factor (k), the coordinate notation will be _______________________________ Ex: Dilate triangle ABC, using the scale factor 3. A (1,1) _________________ = A’ (__________) B (3,1) _________________ = B’ (__________) C (1,3) _________________= C’ (__________) (x,y) => (kx, ky) (3*1, 3*1) (3*3, 3*1) (3*1, 3*3) (3,3) (9,3) (3,9)

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WRITING THE RULE FOR DILATION Find either the ___________________ or the ratios of the corresponding ____________________ Once the scale factor is determined, write the rule in coordinate notation Ex: Scale factor is 3 Rule = ________________ Ex: Scale factor is 1/3 Rule = ________________ scale factor vertices (3x, 3y) (1/3x, 1/3y)

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