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Linear Algebra

Linear Algebra. Tuesday, August 19. Learning Target. I will understand what is meant by slide or translational symmetry and how each point in a figure is related to its image under transformation by translation. Translational Symmetry .

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Linear Algebra

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  1. Linear Algebra Tuesday, August 19

  2. Learning Target I will understand what is meant by slide or translational symmetry and how each point in a figure is related to its image under transformation by translation.

  3. Translational Symmetry • Translation” A transformation that slides each point on a figure to an image point a given distance and direction from the original point. Polygon A′B′C′D′E′ below is the image of polygon ABCDE under a translation. If you drew line segments from two points to their respective image points, the segments would be parallel and they would have the same length.

  4. Translational Symmetry • Transational Symmetry:A design has translational symmetry if you can slide it to a position in which it looks exactly the same as it did in its original position. To describe translational symmetry, you need to specify the distance and direction of the translation. Below is part of a design that extends infinitely in all directions. This design has translational symmetry.

  5. video • http://dashweb.pearsoncmg.com/main.html?r=15512&p=216

  6. 1.3 In a Spin How could you describe a translation that matches the basic design element to an image? • A translation matches any two points X and Y on a figure to points X’ and Y’ so that line segment XY and line segment X’Y’ are the same length and parallel to each other • The figure moves each point X to X’ and Y to Y’ the same distance and direction

  7. 1.3 Sliding Around: Translations A 1. In both diagram 1 and diagram 2 the connecting segments made by connecting corresponding vertices, GG’, HH’, etc. will be equal in length and parallel to each other. A 2. There is no ending point, it could go on infinitely in the direction and distance specified.

  8. 1.3 Sliding Around: Translations B 1. The segments joining points and their images are all the same length as the translation arrow and are parallel to it. • B 2. • Corresponding sides are the same length and parallel. • Corresponding angles are the same measure.

  9. 1.3 Sliding Around: Translations B 3. ABB’A’ is a parallelogram. AB and A’B’ are the same length and parallel. AA’ and BB’ are the same length and parallel to the translation arrow. B 4. SKIP IT!

  10. 1.3 Sliding Around: Translations • In all cases any basic design element plus a transformation (flip, slide, turn) will make an image. • Reflection: one image is needed to complete the design. • Rotation: the number of images depends on the angle of rotation • Translation: the number of images is infinite • IN ALL CASES SIZE AND SHAPE ARE PRESERVED

  11. 1.3 Sliding Around: Translations • A translation matches any two points X and Y on a figure so that…. • Line segment XY and line segment X’Y’ are the same length and parallel to each other. • The figure moves each point X to X’ and Y to Y’ the same distance and direction

  12. Rate your understanding Learning Target I will understand what is meant by slide or translational symmetry and how each point in a figure is related to its image under transformation by translation.

  13. Homework tonight • Complete ACE Questions #11 and #18 starting on page 18 of BPW

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