Dilation (Cartesian) GraphingClassifying Irma Crespo 2010

Raymond’s Warm Up A man copies a picture to a certain size but does not know how big he made it. Get the scale factor of the picture to find how big the picture was made.A man copies a picture to a certain size but does not know how big he made it. Get the scale factor of the picture to find how big the picture was made. original 6 8 a)5 b)8 c)6 d)7 Author: Raymond Morrow April 2010 copy 36 48

Devin’s Warm Up There are two geckos: a mom and a baby. It takes two years for a baby gecko to grow the size of its mom. If the baby gecko is half the size of its 10 inches by 2 inches mom, what is the size of the baby?There are two geckos: a mom and a baby. It takes two years for a baby gecko to grow the size of its mom. If the baby gecko is half the size of its 10 inches by 2 inches mom, what is the size of the baby? 10 inches 2 inches mom a)5 in by 2 in b)20 in by 4 in c)5 in by 4 in d)5 in by 1 in baby Author: Devin Seamans April 2010

Dilation Dilation is enlarging or reducing a figure by a scale factor.Dilation is enlarging or reducing a figure by a scale factor.

Draw a Dilation AD C B Scale Factor: 2 Center Point: A Enlargement of Polygon ABCD D’ C’ B’

Ordered Pairs in Dilation Scale Factor: 2 (0,0) (2,0) (2,2) (0,1)Original Multiply by 2 Multiply by 2Image D(2,0) C(2,2) B(0,1) A(0,0)A(0*2,0*2) B(0 *2,1 *2) C(2 *2,2 *2) D(2 *2,0 *2)D’(4,0) C’(4,4) B’(0,2) A(0,0) (0,2) (4,4) (4,0) ABCDAB’C’D’

On the Graphing Board Plot triangle JKL with the following ordered pairs (x, y) : J(3,8) K(10,6) L(8,2) Plot triangle J’K’L’ with a scale factor of ½.Plot triangle J’K’L’ with a scale factor of ½. JKL Multiply by ½ Multiply by ½ J’K’L’ J’K’L’ J(3,8) K(10,6) L(8,2) ½½ L(8* ½,2* ½) ½½ K(10* ½,6* ½) ½½ J(3* ½,8* ½) L’(4,1) K’(5,3) J’(1.5,4)

On the Graphing Board Plot triangle JKL with the following ordered pairs (x, y) : J(3,8) K(10,6) L(8,2) Plot triangle J’K’L’ with a scale factor of 2.Plot triangle J’K’L’ with a scale factor of 2. ∆JKL Multiply by 2 Multiply by 2 ∆J’K’L’ J(3,8) K(10,6) L(8,2) 2 L(8* 2,2*2) 22 K(10* 2,6* 2) 22 J(3* 2,8* 2) L’(16,4) K’(20,12) J’(6,16)

Find and Classify a Scale Factor Quadrilateral V’Z’X’W’ is a dilation of quadrilateral VZXW.Quadrilateral V’Z’X’W’ is a dilation of quadrilateral VZXW. V’ W’ X’ Z’ Z V X W COPY ORIGINAL

Find the Scale Factor Pick corresponding points (ordered pairs).Pick corresponding points (ordered pairs). Make a ratio of either the Xs or the Ys following:Make a ratio of either the Xs or the Ys following: V’ W’ X’ Z’ Z V X W coordinate point of copy coordinate point of original V(-2,2) and V’(-5,5) V’V OR 5252

Classify the Scale Factor Scale factor isScale factor is V’ W’ X’ Z’ Z V X W 5252 Is it less than 1?Is it less than 1? Is it greater than 1?Is it greater than 1? It is an enlargement.It is an enlargement. So, it is not a reduction.So, it is not a reduction. NO YES

Your Turn Find and Classify the Scale Factor (OHP) B A A’ C C’ B’ Triangle A’B’C’ is a dilation of  ABC.Triangle A’B’C’ is a dilation of  ABC.

Summary Dilation is enlarging or reducing a figure by a scale factor.Dilation is enlarging or reducing a figure by a scale factor. To graph a dilation given ordered pairs and scale factor:To graph a dilation given ordered pairs and scale factor: *multiply the scale factor to each coordinate point of each ordered pair *plot the scaled ordered pairs *connect the points with line segment To find the scale factor, pick corresponding ordered pairs and create the ratio ofTo find the scale factor, pick corresponding ordered pairs and create the ratio of A dilation is an enlargement if the scale factor is greater than 1.A dilation is an enlargement if the scale factor is greater than 1. A dilation is a reduction if the scale factor is less than 1.A dilation is a reduction if the scale factor is less than 1. coordinate point of copy coordinate point of original

Exit Slip Plot line segment XY with the following ordered pairs:Plot line segment XY with the following ordered pairs: X(-4,2)X(-4,2) Y(2,6)Y(2,6) Plot line segment X’Y’ with a scale factor of ½.Plot line segment X’Y’ with a scale factor of ½.. Classify if the dilation is enlargement or reduction. EXPLAIN!Classify if the dilation is enlargement or reduction. EXPLAIN!.

Practice Worksheet Complete the practice worksheet. Work with a partner or on your own. Submit completed worksheet for grading. Solutions are discussed the next day. Skills Practice: Lesson 4-8, Page 54

Main Resources Math Connects: Concepts, Skills, and Problem Solving; Teacher Edition; Course 3, Volume 1 Columbus:McGraw-Hill, PowerPoint created by Irma Crespo. University of Michigan-Dearborn, School of Education. Winter Lesson plan put together by Irma Crespo.