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Reflection PowerPoint Presentation

Reflection

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Reflection

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  1. Reflection Reflection

  2. To reflect harder shapes, we reflect each of their corners separately and then join the reflected points I O Reflection produces congruent shapes

  3. To reflect harder shapes, we reflect each of their corners separately and then join the reflected points O I

  4. Rotation

  5. What is the meaning of Rotation? • Rotate the rectangle: • 90° • Clockwise • About C O c Centre of Rotation I Rotation is a Transformation

  6. What is the meaning of Rotation? • Rotate the triangle: • 90° • Anti-clockwise • About C O I c Rotation produces congruent shapes

  7. Formal Rotation

  8. How do we rotate a shape in general? • Rotate this shape: • 60° • Anti-clockwise • About C O I 60° c

  9. How do we rotate a shape in general? • Rotate this shape: • 60° • Anti-clockwise • About C O I 60° c

  10. Sliding Translation = Horizontal Steps vector Vertical Steps I O

  11. Translate by the vector I O

  12. Translate by the vector I O

  13. Translate by the vector O I

  14. Translate by the vector O I

  15. 01234567891011121314151617181920212223 Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement C Centre of Enlargement

  16. 01234567891011121314151617181920212223 Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement Can you see where the rest of the shape will be? C

  17. 01234567891011121314151617181920212223 Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement Can you see where the rest of the shape will be? C

  18. 01234567891011121314151617181920212223 Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement Can you see where the rest of the shape will be? I 0 C

  19. 01234567891011121314151617181920212223 Enlarge this shape by a scale factor of 3 about the marked centre of enlargement Can you see where the rest of the shape will be? C

  20. 01234567891011121314151617181920212223 Enlarge this shape by a scale factor of 3 about the marked centre of enlargement C

  21. 01234567891011121314151617181920212223 Enlarge this shape by a scale factor of 3 about the marked centre of enlargement C

  22. 01234567891011121314151617181920212223 Enlarge this shape by a scale factor of 3 about the marked centre of enlargement C

  23. Enlarge this shape by a scale factor of 3 about the marked centre of enlargement I C O

  24. The Different Positions of the Centre of Enlargement

  25. The centre of enlargement can lie on a corner of the shape x 4 x 3 x 2 C

  26. The centre of enlargement can lie on a side of the shape x 3 x 2 C

  27. The centre of enlargement can lie inside the shape x 3 x 2 C

  28. Finding The Centre of Enlargement

  29. Where is the centre of enlargement? C O I

  30. Where is the centre of enlargement? I O C

  31. Scale Factor Pairs

  32. x 2 What is the scale factor from A to B? x ½ What is the scale factor from B to A? B C A

  33. x 1 3 What is the scale factor from A to B? x 3 What is the scale factor from B to A? B A C

  34. x x 2 3 3 2 What is the scale factor from A to B? What is the scale factor from B to A? C A B The scale factors which transform object to image and vice versa are always reciprocals of each other

  35. Negative Scale Factors

  36. What is the meaning of a negative scale factor?

  37. Enlarge object A by a scale factor of -1 +ve -ve C A B What is the scale factor from B to A? What other single transformation would have produced the same result from A to B?

  38. Enlarge object A by a scale factor of -1 C A B The Enlargement with scale factor -1 and a given centre of enlargement C is the same as a rotation by 180° about C , and C is also known as centre of symmetry

  39. Enlarge object A by a scale factor of -1 -2 C A B

  40. 1 2 Enlarge object A by a scale factor of -1 -2 C A B What is the scale factor from B to A? What combination of transformations would have produced the same result from A to B?

  41. Summary on Transformations

  42. REFLECTION • Object • Line of reflection • Congruent Image • Orientation is not maintained ROTATION • Object • Centre of Rotation • Direction of Rotation • Amount of Rotation • Congruent Image • Orientation is not maintained TRANSLATION • Object • Vector • Congruent Image • Orientation is maintained ENLARGEMENT • Object • Scale Factor • Centre of Enlargement • Similar Image • Orientation is maintained or • turned “upside down”