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Understanding Transformations: Reflections, Rotations, and Translations in Geometry

Dive into the concepts of transformations in geometry with a focus on rigid and non-rigid transformations. Learn the definitions of reflections, rotations, and translations, and understand how to apply these concepts using coordinate planes. This lesson will include problem-solving with examples and a quiz to reinforce your learning. Resources like videos, worksheets, and interactive activities are provided to enhance your understanding. Stay engaged and track your progress in class while exploring the beauty of geometric transformations!

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Understanding Transformations: Reflections, Rotations, and Translations in Geometry

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  1. D.E.A.R 15 minutes

  2. Do now • Using the figure on the board, solve the problem Lines k and l are parallel What is the value of z? • 130 • 120 • 100 • 80

  3. 2-11-13 • http://youtu.be/gb3yBvDkIMk

  4. Unit 2 Transformations (this PowerPoint will be posted on the class wiki if you miss something)

  5. What is a transformation? • A copy of a geometric figure • The copy holds certain properties (Similar to copy and paste on the computer) • Pre – image = original figure • Image = new (copied) picture

  6. Transformations • 2 basic types: 1. Rigid Transformations • Definition: the pre image and image both have exact same size and shape • 3 types of rigid are: • A. translations • B. reflections • C. rotations 2. Non-rigid transformations

  7. The 2nd type of transformation • Non rigid transformation: • Definition: it can do stretching and shrinking and twisting

  8. Basic Transformation Geometry • http://www.gradeamathhelp.com/transformation-geometry.html • This is a resource, in case you need to refer to later

  9. Polygons and transformations • Describe these shapes with translations, reflections, and rotations OR use the nets • We will use ipad, graph paper, or you will make a coordinate plane • Record in your notebook, the ordered pairs you start with and where you end up: complete a translation and reflection

  10. independent • Which of the following preserves distance which does not? Explain • (x, y) translated with rule (x +1, y + 2) • Or • (x, y) translated with rule (x2, y + 1) • Is distance the same as area or perimeter? • Also, there is a worksheet/assignment on www.kz.com

  11. 2-11-13 • Summary: • How can you represent a transformation in the coordinate plane? • Put answer in your notebook • Date and label

  12. 2-13D.E.A.R 15 minutes

  13. 2-13-13 • Do Now: • Create a venn diagram for the two words • rigid transformation • non-rigid transformation in your notebooks

  14. 2-13-13 • Definitions (in terms of lines parallel or perpendicular, angles, circles, segments) • Reflections • Rotations • Translations

  15. 2-13-13 • Pictures/videos to help with definitions • www.mcescher.com • Soccer passes

  16. Transformation and angles examples • http://www.youtube.com/watch?v=HfdPghAo_y8&feature=share&list=PL672620CA05CCA02A (passes angles and lines) • http://youtu.be/1c7DVV4oP4U • Passing, transformations, and angles • What can you not do in basketball after you stop with the ball? • Consider your planted foot as your rotation point

  17. Tuesday’s work • Read pg. 547 define and understand Composition of transformation • - pg. 549 (7 - 18 even), and #19 • - pg. 550 #27 this will count as a project grade/formal grade 70%, therefore you may want to do this problem last

  18. Tuesday’s work continue • pg. 551 (42, 43, 44) complete the problems and tell me how these 3 problems relate to transformations

  19. 2-14-13 DO NOW 5 minutes • Define reflection • Define translation • D.E.A.R 10 minutes • At the end of today’s D.E.A.R please send me a message/note on edmodo describing your what you read today; you will have 5 minutes

  20. Quiz today • Reflection • Translation • Essay ?: How can you change a figure’s position without changing its size and shape? (Send your answer to me using edmodo, just me not the whole class) • If finish the quiz early, then please read or work quietly on your translation project ( I cannot answer questions, until all students have completed test)

  21. 4th block only: 2-14-13 • Quiz on Thursday • Honors: read article, write synopsis on the article, but they must include the terms in the article • Paragraph, use of proper grammar, math terms, math connections, good spelling, • Type on edmodo and send to me or we will use gaggle

  22. 2-15-13 • Do now: what is the name of the original figure in transformations? What is the name of the new figure?

  23. agenda • Go over yesterday’s test • Give students their scores, results, post those problems that need most work • Work on projects • Wallpaper or wrapping paper (your translation design) • Rotation and reflection worksheets

  24. What do children have to do when they first play with this toy?

  25. 9.1 Translations 1. What does isometry mean? • Congruent 2. What is a rule that describes the two shapes with the following ordered pairs? Q (- 5, 4) Q’ (1, 2) R (- 2, 3) R ‘ (4, 1) T (- 5, -2 ) T ‘ (1, - 4) S ( -3, -1) S ‘ (3, - 3)

  26. 9.1 Translations 3. What are the images of the vertices of ABC for the translation (x, y) translated by the rule ( x – 2 , y + 3)? The vertices are A (5, 6) , B ( 6, - 3), and C (7, 2)

  27. Tuesday’s work continue • Read pg. 553 - 558 define the key terms (reflection, line of reflection) • - pg. 556 #8, 10, 12, 23, and 24 • Then onto Rotations

  28. 9 -2 Reflections • If point D (4, 1) is reflected across x = 2, what are the coordinates of its reflection? A (4, -1) B ( 4, 3) C (- 4, 1) D (0, 1)

  29. 9 – 2 Reflections 2. A design for the math club log reflects a triangle across the y – axis. Graph the reflection. A (2, 4) B (6, 2) C (2, - 6)

  30. 9 -2 Reflections 3. You are building a garden fountain with paths to the rose bushes and the herb garden. You make a graph showing the roses at (5, 5) and the herbs at (3, 2). You want to minimize the length of the brick paths. If the fountain is located on the y-axis, where should it be built? A (0, 7/2) C (0, 4) B (0, 25/8) D (0, 13/2)

  31. Activiy 2-14-13 • Reflections and rotations • Use of patty paper • Compass • Protractor • Goal: how to rotate an object a certain degree and reflecting over the line of reflection

  32. Independent work 2-15-13 • Translation Project: formal grade 70%, therefore you may want to do this problem last • Reflection worksheet • 9-2 puzzle, connect dots • Rotation worksheet • 9-3 practice G • challenge problem or re-teaching worksheet

  33. Summary 2-15-13 • In notebook Answer the following: 1. How can you verify that your rule is correct for a specific transformation? 2. What kind of lines are y = 2 and x = 5 (describe the orientation of the line)

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