Chapter 12 Transformations: Shapes in Motion Table of Contents Reflections – Day 1 ……………………………………………..…………….. Page 1 SWBAT: Graph Reflections in the Coordinate Plane HW: Pages #8 - 10 Translations – Day 2 ……………….……….…………….……..…………….. Page 11 SWBAT: Graph Translations in the Coordinate Plane HW: Pages #15 - 16 Rotations – Day 3…………………………………………..………………….. Page 17 SWBAT: Graph Rotations in the Coordinate Plane HW: Pages #23-24 Dilations/Symmetry – Day 4 …………………………………………….….….. Page 25 SWBAT: Graph Dilations in the Coordinate Plane and Identify Line/Rotational Symmetry HW: Pages #31-34 Review – Day 5 ……………………………………………..……..…………….. Page 35 SWBAT: Graph Transformations in the Coordinate Plane HW: Pages #35-38 Compositions – Day 6……………………..……………………………….…….. Page 39 SWBAT: Graph Compositions in the Coordinate Plane HW: Pages #46-49 Overall Review – Day 7……………………….………………………..………….. Page 50 SWBAT: Graph Transformations in the Coordinate Plane HW: Pages #50-61 TRANSFORMATIONS RULES ………….…………………………………………..Page 62 Reflections – Day 1 An Introduction to Transformations 1 Example 1: Example 2: 2 Reflections A reflection (or flip) is an isometry in which a figure and its image have opposite orientations. Thus, a reflected image in a mirror appears "backwards." Reflections in the Coordinate Plane 1. 3 3. 4. Regents Questions 5. 6. 7. 8. 4 Reflecting Over Vertical and Horizontal Lines 9. 10. 5 Identifying a Reflection Write a rule to describe each transformation. 11. 12. Challenge 6 Summary Exit Ticket 7 Homework for Reflections – Day 1 16. 17. 8 Graphing Reflections 9 Identifying Reflections 10 Translations – Day 2 Warm - Up 1. 2. 11 3. 4. 5. 6. 12 You Try It! 1) Triangle DEF is a translation of triangle ABC. Use the diagram to write a rule for the translation of triangle ABC to Triangle DEF. 2) Pentagon ABCDE is drawn on the grid below. On the grid, draw a translation of pentagon ABCDE using the rule T3,-5. 13 Challenge Summary Exit Ticket 14 Homework 15 16. T5,1 17. T-1, 2 18. T0, -3 19. T4, -4 16 Rotations – Day 3 Warm - Up 1. 2. 17 Notice that degree movement on a unit circle goes in a counterclockwise direction. You will want to remember the layout of the unit circle when you are graphing figures and their rotations. 18 Rules (x, y) R90 = ( ___, ____) R180 = ( ___, ____) R270 = ( ___, ____) Practice 3. 4. ( 9, -1) 5. (-4, -8) 19 Rotations in the Coordinate Plane 9. 90 X’( ___, ____) Y’( ___, ____) Z’( ___, ____) 90 10. 180 180 ***NOTE 20 Practice with a Point Reflection in the Origin Identifying a Rotation Write a rule to describe each transformation. a. b. 21 Challenge Summary Exit Ticket 22 Homework 23 24 Dilations/Symmetry – Day 4 Warm – Up 1. 2. 25 To find the image of a point under a dilation, you multiply each coordinate by the scale factor. 1 1 1 a) D4 (x,y) (4x,4y) b) D (x,y) ( x, Y ) 6 6 6 Example- Find a) D2(3,4) b) D (6,9) 1 3 Dilations in the Coordinate Plane 1. 26 2. Regents Questions 3. 4. 5. 6. 7. 27 28 Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry. Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry. 29 Challenge SUMMARY 30 Homework – Dilations/Symmetry – Day 4 31 22. 23. 32 Symmetry 33 34 Review – Day 5 35 36 37 38 Compositions – Day 6 Warm – Up 1. 2. Which rotation about point O maps B to D? _______ 39 c) 40 Practice Problem #1 You try It! 41 Practice Problem #2 You try It! 42 The symbol for a composition of transformations is an open circle. The notation is read as a reflection in the x-axis following a translation of (x+3, y+4). Be careful!!! The process is done in reverse!! You may see various notations which represent a composition of transformations: could also be indicated by Problem #3 43 You Try It! CHALLENGE 44 SUMMARY Exit Ticket 45 Homework – Compositions – Day 6 1. 2. 3. 46 4. 5. 6. 7. 7. 47 8. 9. 48 10. 49 Review – Day 7 Transformations Review SUMMARY TABLE 50 Section 1: Reflections 51 Line Reflections 52 Section 2: Translations 53 54 Section 3: Rotations 3. Locate and label A’, the image of A under R270 (three quarter-turn about the origin) 55 56 Section 4: Dilations/Symmetry 57 58 Section 5: Compositions 1. 2. fdg 3. 4. 5. Find the composite transformation indicated. 59 6. 7. 60 8. *** Other Properties*** 5. 61 62 .