Adapted from a lesson found at: popehs.typepad,corn

Transcription

1 Diations nvestigationstudent Activity Objective: Given grid paper, a centimeter ruer, a protractor, and a sheet of patty paper the students wi generate and appy the reationship between the scae factor of diation and the coordinates of the image, ange measures, perimeter, and area by competing data tabes and by redrawing figures on graph paper. The student is expected to generate simiar figures using diations incuding enargements and reductions, graph diations, refections, and transations on a coordinate pane, use and extend simiarity properties and transformations to expore and justify conjectures about geometric figures and describe the resuting effects on perimeter and area when dimensions of a shape are changed proportionay. Lesson Overview: n part one, students wi use patty paper to create a diation with a scae factor of two on pane paper. Students wi then transfer the diation to the coordinate grid and create additiona diations of the same figure with scae factors of three and onehaf. n part two, students wi make coordinate diations of severa figures and wi ook at the effect of the scae change on the coordinates, side engths, perimeter, and area of each image. Extension: Students can graph the coordinates of the four trianges in part one using a graphing cacuator and determine the equations for the rays used in the diation. Grouping: Students shoud work in groups so they can discuss with each other what they notice about the effects of the diations. Materias: Each student wi need a copy of the esson, a separate sheet of centimeter grid paper, a centimeter ruer, a protractor, and a sheet of patty paper. Students can the use same piece of patty paper for steps one through eight to transfer the diations to the grid paper. Students shoud be abe to work through the document on their own with teacher guidance. Homework: Students can compete part two of the assignment as homework. Most students shoud be abe to compete both parts in a ninetyminute cass period. Adapted from a esson found at: popehs.typepad,corn

2 Diations nvestigationstudent Activity Name: Diations Part. On the picture beow, draw rays from 0 through each vertex of MBC. 2. Use patty paper to measure the ength of OA. Pace A' on OA so that OA' = 2 OA Geometry 3. Use the same process to find B' and C'. 4. Draw M'B'C'. 5. Trace MBC on a piece of patty paper. Compare the anges of MBC with the anges of M'B'C'. What do you notice about the ange measures? 6. Use a ruer to find the foowing engths in centimeters. a. AB= d. A'B' = b. BC= e. B'C'= c. AC= f. A'C' = 7. What do you notice about the engths of the sides of the two trianges? 8. The Scae Factor for this diation is _ A B c 0

3 Diations nvestigationstudent Activity 9. Use your patty paper to transfer MBC and M B C to the grid paper with point 0 at the origin. Write the ordered pairs next to each vertex on the grid paper and in Tabe beow. What do you notice about these ordered pairs? 0. Diate MBC using a scae factor of 3 on your grid paper. Labe the new triange M" B"C". Write the ordered pairs next to each vertex and in Tabe beow.. Diate MBC using a scae factor of..!_ on your grid paper. Labe the triangem"'b"'c"'. Write the 2 ordered pairs next to each vertex and in Tabe beow. Tabe Ordered Pairs Origina Triange Diation (Scae Factor of2) Diation (Scae Factor of 3) Diation (Scae Factor of ) 2 A A' A" A"' B B' B" B"' c C' C" C"' 2. What observations/conjectures can you make about diations and ordered pairs based on your work so far? 3. Compete this conjecture based on Tabe : The image of (a, b) after a diation with center 0 and scae factor k has coordinates ( ).

4 Diations nvestigationstudent Activity Name: Diations Part " Record your observations about the characteristics of the trianges MBC and M'B'C' from Diations Part in the tabe beow. Characteristics Origina MBC Coordinates A(3, 5) B(3, 2), C(7, 2) Ange Measures Length of Sides Perimeter Area M'B'C' (Scae Factor of 2) Observations Geometry 2, Graph Quadriatera JKLM on the back of your grid paper (from Part ). Diate quadriatera JKLM with a scae factor of 3 on your grid paper. Labe the image J 'K' L'M' and compete the tabe beow. Characteristics Origina JKLM Quad. J'K'L'M' _(Scae Factor of3) Observations Coordinates J(2, ) K(2, 3), L(3, 3), M(3, ) Ange Measures Length of Sides Perimeter Area,.,3,. Graph Quadriatera QRST on the same grid paper. Diate quadriatera QRST with a scae factor of.!.. on your grid paper. Labe the image Q' R' S 'T' and compete the tabe beow. 2 Quad. Q'R'S'T' Characteristics Origina QRST (Scae Factor of Observations ) 2 Q(2,2) R(2, 4), Coordinates S(6, 4), T(6, 2) Ange Measures Length of Sides Perimeter Area

5 Diations nvestigationstudent Activity A diameter of a circe has endpoints A and B. Graph the circe on your grid paper. Diate the circe W'th a seae f:actor of2 Labe the coordm' ates of the r.mage A' and B' and comp.ete thetabe beow. Origina circe with New circe with Characteristics Observations diameter AB diameter A' B' Coordinates Length of the diameter Length of the radius Circumference Area A(4,), B(4,3) JJ.Based on the information in a four tabes, what conjectures can you make about: e. Scae Factor used in the diation and ange measures f. Scae Factor used in the diation and side engths/diameter. g. Scae Factor used in the diation and perimeter/circumference. h. Scae Factor used in the diation and area. ""Use the graph to beow to answer the foowing diation questions. rrr 8 r ṇ.., with a scae factor of 3. 6 =t " r 4... \... :;!'"", 0 a) Find the coordinates of triange A' B' C' after a diation... How does this change ange measures? ""'..., )"... ' r 4 2 f 6 b) Find the coordinates of triange A' B' C' after a diation with a scae factor of 2. 8 How does this change the engths of the sides? D=" r i c) fthe coordinates of A' are (.5, ) after a diation, find the coordinates of B' and C'? How does this change the perimeter of the triange? d) f the coordinates of B' are (8, 2) after a diation, find the coordinates of A' and C'?

6 Diations nvestigationstudent Activity Name: How does this change the area of the triange? Geometry

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