1. Transformations Learning Outcomes  I can translate, reflect, rotate and enlarge a shape  I can enlarge by fractional and negative scale factors  I can interpret diagrams where transformations have occurred  I can find the centre and scale factor of a given enlargement  I can find the centre direction and angle of a given rotation

2. Transformations Reflection The object and its image are always the same perpendicular distance from the mirror line. A B C x axis y axis

3. Transformations Reflection Reflect triangle ABC in the line y = x. A B C y = x

4. Transformations Reflection Reflect triangle ABC in the line y = -x. A B C y = -x

5. Transformations Reflection Summary of Reflections Object pointsReflectionImage Points A(1,1) B(1, 3) C(2,2) D(1, 2) x axis A(1,-1) B(1, -3) C(2,-2) D(1, -2) ( x, y ) → ( x, -y ) A(1,1) B(1, 3) C(2,2) D(1, 2) y axis A(-1,1) B(-1, 3) C(-2,2) D(1-, 2) ( x, y ) → ( -x, y ) A(1,1) B(1, 3) C(2,2) D(1, 2) y = x A(1,1) B(3, 1) C(2,2) D(2, 1) ( x, y ) → ( y, x ) A(1,1) B(1, 3) C(2,2) D(1, 2) y = -x A(-1,-1) B(-3, -1) C(-2,-2) D(-2, -1) ( x, y ) → ( -y, -x )

6. Transformations Rotations Rotation of 90° clockwise about (0, 0) A B C

7. Transformations Rotations Summary of Rotations ObjectImage A (1, 1) A ' (1, -1) B (1, 3) B ' (3, -1) C (2, 2) C ' (2, -2) D (1, 2) D ' (2, -1) (x, y) → (y, -x) ObjectImage A (1, 1) A ' (-1, -1) B (1, 3) B ' (-1, -3) C (2, 2) C ' (-2, -2) D (1, 2) D ' (-1, -2) (x, y) → (-x, -y) ObjectImage A (1, 1) A ' (-1, 1) B (1, 3) B ' (-3, 1) C (2, 2) C ' (-2, 2) D (1, 2) D ' (-2, 1) (x, y) → (-y, x) 90º Clockwise at (0,0) 180º (either direction) at (0,0) 90º Anti-Clockwise at (0,0)

8. Transformations Translations When a shape is translated its orientation does no change – it looks the same but is in a different position. A translation is written as a column vector with x denoting the number of units the shape is moved along the x axis and y denoting the number of units the shape is moved along the y axis. +ve - ve A translation moves a shape 5 units to the right and 2 units up. A B C

9. Transformations Translations 1.Translate ABCE label the new shape A 1 B 1 C 1 D 1 2.Translate A 1 B 1 C 1 D 1 label the new shape A 2 B 2 C 2 D 2 A B D C A1A1 B1B1 D1D1 C1C1 A2A2 B2B2 D2D2 C2C2

10. Transformations Enlargements An enlargement has 2 properties 1) Centre 2) Scale Factor When a shape is enlarged the image point is found by using the centre and scale factor of the enlargement Point Centre Point Scale Factor Image AA 1 (6, 6) BB 1 (18, 6) CC 1 (18, 12) With following table shows and enlargement with centre (0, 0) and scale factor 3

11. Transformations Enlarging a Shape when centre of Enlargement is not origin A B D C PointCentre → PointImage Point Enlarge shape ABCD by scale factor 3 centred at (-1, 2)

12. Transformations Enlarging a Shape when centre of Enlargement is not origin -4 -2 0 2 -6 5 10 -10 -5 PointCentre → PointImage Point Enlarge shape ABCD by scale factor -2 centred at (0, 0)

13. Additional Notes

15. Transformations Learning Outcomes: At the end of the topic I will be able to Can Revise Do Further          I can translate, reflect, rotate and enlarge a shape  I can enlarge by fractional and negative scale factors  I can interpret diagrams where transformations have occurred  I can find the centre and scale factor of a given enlargement  I can find the centre direction and angle of a given rotation 