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2. Intro Rotations An object can be rotated to a new position. To describe the rotation fully, you need to specify: (1) The centre of rotation. (2) The direction of rotation (Clockwise (CW) or Ant-Clockwise (ACW)). (3) The angle of rotation. A A’ This grid shows that A has been rotated 90 o ACW about P to A’. P P A A’ This grid shows that A has been rotated 90 o CW about P to A’.

3. Rotations On the grid below, triangle T has been rotated 90 o ACW about the origin (0,0) to T’ and 180 o CW about the origin to T’’. Note that a 180 ACW rotation would still transform T to T’’. y T T’ T’’

4. Rotations Tracing paper can help you in rotating an object about a given point. In the example below the triangle is to be rotated 90 o ACW about the origin. y 1. Draw shape. 2. Hold pencil point firmly on centre of rotation and turn paper through required angle.

5. Tracing paper can help you in rotating an object about a given point. In the example below the triangle is to be rotated 90 o ACW about the origin. y 1. Draw shape. 2. Hold pencil point firmly on centre of rotation and turn paper through required angle.

6. Rotations In this example the kite is to be rotated 180 o CW about point (1,1). y 1. Draw shape. 2. Hold pencil point firmly on centre of rotation and turn paper through required angle.

7. Rotations In this example the kite is to be rotated 180 o CW about point (1,1). y 1. Draw shape. 2. Hold pencil point firmly on centre of rotation and turn paper through required angle.

8. Q1/2 Rotations Question 1. Rotate the rectangle R, 90 o CW about (0,0) and mark as R’ y R Q Question 2. Rotate the quadrilateral Q, 180 o about (-1,1) and mark as Q’ R’ Q’

9. Rotations To find the centre of rotation use trial and improvement by holding the pencil firmly on a point that you think may be the centre of rotation then turn the tracing paper until object and image coincide. Remember a ¼ turn of the tracing paper equates to an angle of 90 o whereas a ½ turn equates to 180 o. y T T’ x x x x x x x In this case the transformation is a clockwise rotation of 90 o about the point (-3,2)

10. Q3/4 Rotations Question 3. Describe fully the transformation that takes R to R’. y Q Q’ Question 4. Describe fully the transformation that takes Q to Q’. A rotation of 180 o about the point (1,1) An ACW rotation of 90 o about point (-1,0) R R’

11. Question 1. Rotate the rectangle R, 90 o CW about (0,0) and mark as R’ Question 2. Rotate the quadrilateral Q, 180 o about (-1,1) and mark as Q’

12. Question 3. Describe fully the transformation that takes R to R’. Question 4. Describe fully the transformation that takes Q to Q’. x 024 6 -2 -4 -6 2 4 -2 -4 T 1 3 -3 13 5 -3 -5 y Q Q’ R R’