Rotation

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

2. 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.

3. Rotation • Centre of rotation 90o • Angle of rotation clockwise • Direction of rotation Put a piece of tracing paper over the drawing Copy the object onto the tracing paper A A’ Put a pencil on the tracing paper – point at the centre of rotation X 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.

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

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

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

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

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