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

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GRAB TEXTBOOKS TEAR OUT PAGES ; GRAB WS AND STAPLE TOGETHER

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.

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

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

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 preimage. corresponding side lengths numerator denominator

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

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

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 Scale factor of 2; Enlargement

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)

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)