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### Paper 2

TRANSFORMATION GEOMETRY
Investigate, generalise and apply the effect on the co-ordinates of:
(a) the point (x ; y) after rotation around the origin through an angle of 90º or 180º;
(b) the vertices
(x1 ; y1),
(x2 ; y2),...
(xn ; yn)
of a polygon after enlargement through the origin, by a constant factor k.

(a) Use the compound angle identities to generalise the effect on the co-ordinates of a point (x ; y) after rotation about the origin through an angle θ.
(b) Demonstrate the knowledge
· that rigid transformations (translations, reflections, rotations and glide reflections) preserve shape and size,
· and that enlargement preserves shape but not size.

Clarification

• Transformations & Enlargements
- Determine the rule of transformations that has occurred.
- Determine the factor of a dilation (enlargement or reduction).
- The factor of dilation is an element of the rational numbers.
- Use a transformation rule to sketch images of transformations of shapes, determine points of the image of a transformation of a shape and determine the relationship of the area of the image in relation to its original shape.
• Rotations that are generated in
- an anticlockwise direction are regarded as positive whilst
- clockwise rotations are regarded as negative.