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Transformations and Symmetry

Transformations and Symmetry. Vocabulary. Image – The result of moving all points of a figure according to a transformation Transformation – The rule that assigns to each point of a figure another point in the plane. Vocabulary.

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Transformations and Symmetry

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  1. Transformations and Symmetry

  2. Vocabulary • Image – The result of moving all points of a figure according to a transformation • Transformation – The rule that assigns to each point of a figure another point in the plane

  3. Vocabulary • Rigid Transformation, Isometry – The image is congruent to the original figure • Nonrigid Transformation – A transformation that does not preserve the size and the shape

  4. Translation • Translation – An isometry where each point is moved by the same translation vector

  5. Translation

  6. Rotation • Rotation – An isometry in which each point is moved by the same angle measure in the same direction along a circular path about a fixed point

  7. Rotation Rotation with Patty Paper

  8. Reflection • Reflection – An isometry in which each point and its image are on opposite sides and the same distance from a fixed line

  9. Reflection

  10. Investigation • Get your supplies Straight Edge Patty Paper

  11. Investigation • Draw a polygon and a line of reflection next to it on a piece of patty paper

  12. Investigation • Fold your patty paper along the line of reflection and create the reflected image of your polygon by tracing it

  13. Investigation • Draw segments connecting each vertex with its image point. • What conclusion can you draw comparing the segments and the line of reflection

  14. Investigation • Conjecture • The line of a reflection is the perpendicular bisector of every segment joining a point in the original figure with its image

  15. Vocabulary • Reflectional Symmetry – The property that a figure coincides with itself under a reflection (mirror symmetry) • Line of Symmetry – The line of reflection of a figure having reflectional symmetry

  16. Vocabulary • Rotational Symmetry – The property that a figure coincides with itself under some rotation • Point Symmetry – The property that a figure coincides with itself under a rotation of 180°

  17. Vocabulary • N-Fold Rotational Symmetry – When the angle of rotation can be expressed as 360/n, for a positive value of n

  18. Properties of Isometries

  19. Vocabulary • Ordered Pair Rules – A rule that describes how to transform points on a coordinate plane

  20. Transformation - Example

  21. Investigation • Get your supplies Graph paper Patty Paper

  22. Investigation Fold the graph paper both hot dog and hamburger

  23. Investigation Fold the graph paper both hot dog and hamburger

  24. Investigation

  25. Investigation

  26. Conjectures The ordered pair rule (x,y) →(-x,y) is a reflection across the y-axis The ordered pair rule (x,y) →(x,-y) is a reflection across the x-axis The ordered pair rule (x,y) →(-x,-y) is a rotation about the origin The ordered pair rule (x,y) →(y,x) is a reflection across the line y = x

  27. Homework 7-1 page 372 #1-6, 12-16 7-2 page 381 #1-8, 13-17

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