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.

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Presentation transcript:

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

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

Q1/2 Rotations Rectangle R has been rotated 180 o about the origin (0, 0) y R Q If quadrilateral Q is rotated 180 o about the origin, which quadrant will it end up in? R’ Q’

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. A B Object x2 3 2 A’ Image B’ Image 8 6 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.

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 x3 A’ Image A

Fractional 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. B’ Image A’ Image x½ A Object B x½

This year we will be focusing on dilatations that have a centre of enlargement at (0, 0) Centre of Enlargement Object A B C D Or Count Squares Image A/A/ B/B/ C/C/ D/D/ Dilatations From A Given Point 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. X2

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