1. Rotation Objectives: Rotate shapes about the origin Describe rotations fully about the origin Identify reflection symmetry in 3-D solids Rotate shapes about any point Describe rotations fully about any point Find the centre of rotation and describe it fully

2. For a Rotation, you need An angle or degree of turn –Eg 90° or a Quarter Turn –E.g. 180 ° or a Half Turn A direction –Clockwise –Counter- clockwise A Centre of Rotation –A point around which Object rotates

3. y x 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 -1 -2-2 -3-3 -4-4 -5-5 -6-6 A Rotation of 90° Anticlockwise about (0,0) x x x x x

4. y x 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 -1 -2-2 -3-3 -4-4 -5-5 -6-6 A Rotation of 180° about (0,0) x x x x x x x x

5. Rotation In order to rotate an object we need 3 pieces of information Centre of rotation Angle of rotation Direction of rotation In order to find the image, using this information it is best to use tracing paper.

6. Rotation Centre of rotation Angle of rotation Direction of rotation X 90 o clockwise Put a piece of tracing paper over the drawing Copy the object onto the tracing paper Put a pencil on the tracing paper – point at the centre of rotation Rotate the tracing paper by the required amount in the specified direction Note the end point of the object. Remove the tracing paper and draw the image and label it. A A’

7. Rotation Centre of rotation Angle of rotation Direction of rotation X 30 o clockwise If you are asked to rotate and object by an angle that you have to measure follow the same steps and: A A’ Mark a line from the centre of rotation to use as 0 o and also mark this on the same place on the tracing paper. Before putting the tracing paper on measure the required angle, and draw a line accordingly. 30 o

8. Rotation Now do these y-axis 0 1234567 8 9 10 x-axis 10 -4 -5 -6 -7 -8 -9 -10 -3 -2 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 Rotate A : a)90 o c/w about the origin and label it ‘a’ b)180 o c/w about the origin and label it ‘b’ c)90 o anti c/w about the origin and label it ‘c’ d)90 o c/w about the (2,2) and label it ‘d’ e)90 o anti c/w about the (-2,1) and label it ‘e’ f)90 o anti c/w about the (-4,6) and label it ‘f’ g)90 o anti c/w about the (1,8) and label it ‘g’ A a b c d x x x e x f x g

9. Rotation Finding the centre of rotation Object Draw a line from each point to the corresponding point on the image. B C A C’ B’ A’ Draw the perpendicular bisector for the connecting lines. x The centre of rotation is where the perpendicular bisectors cross. The alternative (easier) method is to trace the object onto tracing paper and use trial and error Image 75 o 75 o anticlockwise

10. Rotation Now do these Find the centre of rotation for each of these rotations a)A onto B b)A onto C c)A onto D d)D onto B e)B onto F f)A onto E g)C onto G h)H onto A i)B onto E j)D onto C y-axis 0 1234567 8 9 10 x-axis 10 -4 -5 -6 -7 -8 -9 -10 -3 -2 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 A B F G H C D 90 o c/w centre (0,0) 180 o c/w or ac/w centre (0,0) 270 o c/w or 90 o ac/w centre (0,0) 90 o c/w centre (2, - 2) E 90 o ac/w centre (2,6) 90 o c/w centre ( - 2, - 1) 180 o c/w or ac/w centre (0,4) 180 o c/w or ac/w centre (4,2) 90 o ac/w centre (0,0)

11. Rotation Rotate shape A : a)90 o c/w about the origin and label it ‘a’ b)180 o c/w about the origin and label it ‘b’ c)90 o anti c/w about the origin and label it ‘c’ d)90 o c/w about the (2,2) and label it ‘d’ e)90 o anti c/w about the (-2,1) and label it ‘e’ f)90 o anti c/w about the (-4,6) and label it ‘f’ g)90 o anti c/w about the (1,8) and label it ‘g’ A 34567 8 9 10 -9 -8 -7 -6 -5 -4 -3 -10 0 12 -2 10 1 2 3 4 5 6 7 8 9 -4 -5 -6 -7 -8 -9 -10 -3 -2 34567 8 9 10 -9 -8 -7 -6 -5 -4 -3 -10 0 12 -2 10 1 2 3 4 5 6 7 8 9 -4 -5 -6 -7 -8 -9 -10 -3 -2 A B F G H C D Find the centre of rotation for each of these rotations a)A onto B b)A onto C c)A onto D d)D onto B e)B onto F f)A onto E g)C onto G h)H onto A i)B onto E j)D onto C Worksheet 1