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Intro

Rotations. Intro.

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Intro

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  1. Rotations Intro 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 Counter-Clockwise (CCW)). (3) The angle of rotation. This grid shows that A has been rotated 90o CCW about P to A’. This grid shows that A has been rotated 90o CW about P to A’. A A A’ A’ P P

  2. 4 3 T 2 1 x 6 5 -6 -5 -2 0 1 2 3 4 -1 -4 -3 -1 -2 -3 -4 Rotations On the grid below, triangle T has been rotated 90o CCW about the origin (0,0) to T’ and 180o CW about the origin to T’’. Note that a 180o CCW rotation would still transform T to T’’. y T T’ T’’

  3. 4 3 T 2 1 x 6 5 -6 -5 -2 0 1 2 3 4 -1 -4 -3 Q’ -1 -2 R’ -3 -4 Rotations Q1/2 Rectangle R has been rotated 180o about the origin (0, 0) If quadrilateral Q is rotated 180o about the origin, which quadrant will it end up in? y R Q

  4. 6 x2 4 A’ Image x2 8 B’ Image 6 Dilatations If a shape (object) is enlarged in such a way that all lengths become twice the size they were on the original, then we say that the shape has been dilatated by a SCALE FACTOR of x2. We say that the rectangle A has been dilatated by a scale factor of x2 to become image A’. Similarly B’ is the image of triangle B after a x2 dilatation. 3 2 A Object 4 B Object 3

  5. Image 12 A’ 6 x3 4 2 15 5 Dilatations In a similar manner, if a shape (object) is enlarged in such a way that all lengths become three times the size they were on the original, then we say that the shape has been dilatated by a SCALE FACTOR of x3. Object A

  6. Fractional 3 6 2 A’ 4 x½ Image 8 4 B’ x½ Image 3 6 Dilatations Fractional Scale Factors If a shape (object) is dilatated in such a way that all lengths become ½ the size they were on the original, then we say that the shape has been dilatated by a SCALE FACTOR of x½. A Object B Object

  7. X2 Dilatations From A Given Point This year we will be focusing on dilatations that have a centre of enlargement at (0, 0) B/ A/ Image D/ C/ A B Object C D Or Count Squares Centre of Enlargement If rays are drawn from the centre of dilatation through each of the vertices of the original object, they will also pass through the vertices of the image.

  8. 1/3 Fractional Enlargements From A Given Point B A Object D C A’ B’ Image D’ C’ Centre of Enlargement

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