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

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

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

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

8. Formal Rotation

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

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

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

13. Translate by the vector O I

14. O I

15. O I

16. O I

18. Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Centre of Enlargement

19. Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Can you see where the rest of the shape will be?

20. Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement C Can you see where the rest of the shape will be? 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

21. Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement C 0 I 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Can you see where the rest of the shape will be?

22. Enlarge this shape by a scale factor of 3 about the marked centre of enlargement C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Can you see where the rest of the shape will be?

23. Enlarge this shape by a scale factor of 3 about the marked centre of enlargement C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

24. Enlarge this shape by a scale factor of 3 about the marked centre of enlargement C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

25. Enlarge this shape by a scale factor of 3 about the marked centre of enlargement C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

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

27. The Different Positions of the Centre of Enlargement

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

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

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

31. Finding The Centre of Enlargement

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

33. C O I

34. Scale Factor Pairs

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

36. C B A What is the scale factor from A to B? What is the scale factor from B to A? x 1313 x 3

37. What is the scale factor from A to B? What is the scale factor from B to A? x 2323 B A C x 3232 The scale factors which transform object to image and vice versa are always reciprocals of each other

38. Negative Scale Factors

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

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

41. A B C 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

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

43. A C Enlarge object A by a scale factor of -1 -2 B What is the scale factor from B to A? What combination of transformations would have produced the same result from A to B? – 1212

44. Summary on Transformations

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