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Objectives:

Objectives:. Recognise and visualise transformations – reflection, rotation and translation. Vocabulary:. rotation. translation. reflection. WARM UP. What is a symmetry? How do you decide if a figure has a line of symmetry? What is a polygon? Name 3 quadrilaterals.

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Objectives:

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  1. Objectives: • Recognise and visualise transformations – reflection, rotation and translation. Vocabulary: rotation translation reflection

  2. WARM UP • What is a symmetry? • How do you decide if a figure has a line of symmetry? • What is a polygon? • Name 3 quadrilaterals. • Name 3 types of triangles and draw them. • Name 4 types of angles and draw them

  3. Types of Transformations

  4. Transformers, more than meet the eye . . . These amazing machines could transform from cars and planes into robots!

  5. What is a transformation? • A transformation is most often called a mapping. • A transformation maps a preimage onto an image. Image Preimage

  6. Task: Draw a 1 by 2 right-angled triangle in different positions and orientations on 5 by 5 spotty paper. Choose one of the triangles to be the original. Describe fully the transformations from your original to each of the other triangles drawn.

  7. See It. DEFC is CCW. D’E’F’C’ is CW.

  8. News FLASH Not All Transformations Yield Congruent Figures

  9. S Size Transformations • Size transformations change the size and sometimes shape of the figure. • The image and pre-image are not congruent. Large Brett Small Brett

  10. Reflection • Produce an object’s mirror image • A reflection must have a mirror line

  11. Reflection Click on this trapezoid to see reflection. The result of a figure flipped over a line.

  12. Reflections and Line Symmetry • A figure in the plane has a line of symmetry if the figure can be mapped onto itself by a reflection in the line. • Example 4: Finding Lines of Symmetry Hexagons can have different lines of symmetry depending on their shape.

  13. Reflections and Line Symmetry This hexagon has one line of symmetry.

  14. Reflections and Line Symmetry This hexagon has four lines of symmetry.

  15. Reflections and Line Symmetry This hexagon has six lines of symmetry.

  16. Now what? • Use the formula to find the angle that the mirrors must be placed for the image of a kaleidoscope to resemble a design. There are 3 lines of symmetry. So you can write 3( mA) = 180° 3x = 180 X = 60°

  17. Now what? • Use the formula to find the angle that the mirrors must be placed for the image of a kaleidoscope to resemble a design. There are 4 lines of symmetry. So you can write 4( mA) = 180° 4x = 180 X = 45°

  18. Now what? • Use the formula to find the angle that the mirrors must be placed for the image of a kaleidoscope to resemble a design. There are 6 lines of symmetry. So you can write 6( mA) = 180° 6x = 180 X = 30°

  19. Which is the true reflection symmetric figure(s)? X C Yes Yes N A No Yes

  20. Rotation(Turn) The action of turning a figure around a point or a vertex.

  21. Click the triangle to see rotation Turning a figure around a point or a vertex Rotation

  22. Translation (Slide) The action of sliding a figure in any direction.

  23. Click the Octagon to see Translation. Translation The act of sliding a figure in any direction.

  24. Reflection (flip) The result of a figure flipped over a line.

  25. Which shapes show reflection, translation, or rotation? Reflection Rotation Translation

  26. Rotation • To rotate an object means to turn it around • Every rotation must have a center and an angle

  27. Translation • Move it without rotating or reflecting it • Every translation has a direction and a distance

  28. Glide Reflection • Involves more than one step • Combination of a reflection and a translation along the direction of the mirror line

  29. Group Activity • Choose a letter (other than R) with no symmetries • On a piece of paper perform the following tasks on the chosen letter: • rotation • translation • reflection • glide reflection

  30. Questions • What happens if you do the same transformation twice? • How many combinations of two transformations are there? • What happens if you combine more than two transformations?

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