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Reflection

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

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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”

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