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## Reflection

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**Reflection**Reflection**To reflect harder shapes, we reflect each of their corners**separately and then join the reflected points I O Reflection produces congruent shapes**To reflect harder shapes, we reflect each of their corners**separately and then join the reflected points O I**What is the meaning of Rotation?**• Rotate the rectangle: • 90° • Clockwise • About C O c Centre of Rotation I Rotation is a Transformation**What is the meaning of Rotation?**• Rotate the triangle: • 90° • Anti-clockwise • About C O I c Rotation produces congruent shapes**Formal**Rotation**How do we rotate a shape in general?**• Rotate this shape: • 60° • Anti-clockwise • About C O I 60° c**How do we rotate a shape in general?**• Rotate this shape: • 60° • Anti-clockwise • About C O I 60° c**Sliding**Translation = Horizontal Steps vector Vertical Steps I O**01234567891011121314151617181920212223**Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement C Centre of Enlargement**01234567891011121314151617181920212223**Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement Can you see where the rest of the shape will be? C**01234567891011121314151617181920212223**Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement Can you see where the rest of the shape will be? C**01234567891011121314151617181920212223**Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement Can you see where the rest of the shape will be? I 0 C**01234567891011121314151617181920212223**Enlarge this shape by a scale factor of 3 about the marked centre of enlargement Can you see where the rest of the shape will be? C**01234567891011121314151617181920212223**Enlarge this shape by a scale factor of 3 about the marked centre of enlargement C**01234567891011121314151617181920212223**Enlarge this shape by a scale factor of 3 about the marked centre of enlargement C**01234567891011121314151617181920212223**Enlarge this shape by a scale factor of 3 about the marked centre of enlargement C**Enlarge this shape by a scale factor of 3 about the marked**centre of enlargement I C O**The Different Positions**of the Centre of Enlargement**The centre of enlargement can lie on a corner of the shape**x 4 x 3 x 2 C**The centre of enlargement can lie on a side of the shape**x 3 x 2 C**The centre of enlargement can lie inside the shape**x 3 x 2 C**Finding The**Centre of Enlargement**x 2**What is the scale factor from A to B? x ½ What is the scale factor from B to A? B C A**x**1 3 What is the scale factor from A to B? x 3 What is the scale factor from B to A? B A C**x**x 2 3 3 2 What is the scale factor from A to B? What is the scale factor from B to A? C A B The scale factors which transform object to image and vice versa are always reciprocals of each other**Negative**Scale Factors**Enlarge object A by a scale factor of -1**+ve -ve C A B What is the scale factor from B to A? What other single transformation would have produced the same result from A to B?**Enlarge object A by a scale factor of -1**C A B The Enlargement with scale factor -1 and a given centre of enlargement C is the same as a rotation by 180° about C , and C is also known as centre of symmetry**–**1 2 Enlarge object A by a scale factor of -1 -2 C A B What is the scale factor from B to A? What combination of transformations would have produced the same result from A to B?**Summary**on Transformations**REFLECTION**• Object • Line of reflection • Congruent Image • Orientation is not maintained ROTATION • Object • Centre of Rotation • Direction of Rotation • Amount of Rotation • Congruent Image • Orientation is not maintained TRANSLATION • Object • Vector • Congruent Image • Orientation is maintained ENLARGEMENT • Object • Scale Factor • Centre of Enlargement • Similar Image • Orientation is maintained or • turned “upside down”