
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”