To reflect harder shapes we reflect each of

To reflect harder shapes, we reflect each of their corners separately and then join the reflected points O I 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 n o i t ta t Cen Ro f o re 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

Translation = Sliding vector Horizontal Steps Vertical Steps O I

Translate by the vector I O

Translate by the vector I O

Translate by the vector O I

Translate by the vector O I

14 0 C 1 2 3 4 5 6 7 8 9 10 11 12 13 Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement Cen Enl tre of arg em ent

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 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1

Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Can you see where the rest of the shape will be? 23

Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement I 0 C 0 1 2 3 4 Can you see where the rest of the shape will be? 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

14 0 1 C 2 3 4 5 6 7 8 9 10 11 12 13 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?

21 22 Enlarge this shape by a scale factor 9 of 20 3 about the 1 18 marked centre of enlargement 17 1 C 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Enlarge this shape by a scale factor of 3 about the marked centre of enlargement C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Enlarge this shape by a scale factor of 3 about the marked centre of enlargement C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1

Enlarge this shape by a scale factor of 3 about the marked centre of enlargement C O I

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 C x 2 x 3

The centre of enlargement can lie inside the shape C x 2 x 3

Finding The Centre of Enlargement

Where is the centre of enlargement? C O I

Where is the centre of enlargement? I O C

Scale Factor Pairs

What is the scale factor from A to B? x 2 What is the scale factor from B to A? x½ C A B

What is the scale factor from A to B? x 3 What is the scale factor from B to A? 1 x 3 A C B

What is the scale factor from A to B? 3 x 2 What is the scale factor from B to A? x 23 C A B The scale factors which transform object to image and vice versa are always reciprocals of each other

Negative Scale Factors

What is the meaning of a negative scale factor?

Enlarge object A by a scale factor of -1 +ve -ve C B A 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 B A 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

Enlarge object A by a scale factor of -1 -2 C B A

Enlarge object A by a scale factor of -1 -2 C A B 1 2 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”