© T Madas
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 rectangle by a scale factor of 2 about the marked centre of enlargement C Centre of Enlargement © T Madas
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 18 19 20 21 22 23 © T Madas
Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Can you see where the rest of the shape will be? C © T Madas
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 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 © T Madas
Why is the centre of enlargement important? 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 © T Madas
Why is the centre of enlargement important? 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 18 19 20 21 22 23 © T Madas
Why is the centre of enlargement important? 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 18 19 20 21 22 23 © T Madas
Why is the centre of enlargement important? 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 18 19 20 21 22 23 © T Madas
Why is the centre of enlargement important? To enlarge a shape you need: A Scale Factor Centre of Enlargement C (Size) (Position) I © T Madas
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 Can you see where the rest of the shape will be? C © T Madas
Enlarge this shape by a scale factor of 3 about the marked centre of enlargement 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 C © T Madas
Enlarge this shape by a scale factor of 3 about the marked centre of enlargement 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 © T Madas
Enlarge this shape by a scale factor of 3 about the marked centre of enlargement 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 © T Madas
Enlarge this shape by a scale factor of 3 about the marked centre of enlargement © T Madas
The Different Positions of the Centre of Enlargement © T Madas
The centre of enlargement can lie on a corner of the shape x 4 x 3 x 2 C © T Madas
The centre of enlargement can lie on a side of the shape x 3 x 2 C © T Madas
The centre of enlargement can lie inside the shape x 3 x 2 C © T Madas
Formal Enlargement on square paper © T Madas
If you are using square paper you can use the following method to enlarge: Scale factor 3 C © T Madas
If you are using square paper you can use the following method to enlarge: Scale factor 3 2 4 x 3 C 6 12 © T Madas
Finding The Centre of Enlargement © T Madas
Where is the centre of enlargement? © T Madas
Where is the centre of enlargement? © T Madas
Scale Factor Pairs © T Madas
x 2 x ½ B A C What is the scale factor from A to B? What is the scale factor from B to A? C B A © T Madas
x 3 B x A C What is the scale factor from A to B? What is the scale factor from B to A? B x 1 3 A C © T Madas
What is the scale factor from A to B? x 3 2 What is the scale factor from B to A? x 2 3 C A B The scale factors which transform object to image and vice versa are always reciprocals of each other © T Madas
Negative Scale Factors © T Madas
What is the meaning of a negative scale factor? © T Madas
-ve +ve A B C What is the scale factor from B to A? 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? © T Madas
Enlarge object A by a scale factor of -1 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 © T Madas
Enlarge object A by a scale factor of -1 -2 C A B © T Madas
A B – C What is the scale factor from B to 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? © T Madas
© T Madas
Enlarge the triangle shown below by a scale factor of 3, with centre of enlargement the origin. 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 © T Madas
© T Madas
Enlarge the triangle shown below by a scale factor of 2½, with centre of enlargement the point P. 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 P © T Madas
© T Madas
Enlarge the trapezium shown below by a scale factor of ½, with centre of enlargement the origin. 10 8 6 4 2 -2 -4 -6 -8 5 1 3 7 9 11 12 13 14 15 -5 -10 -1 -3 -7 -9 -11 © T Madas
© T Madas
R Q P Shape P is enlarged to give shape Q. One side of shape Q is drawn for you. What is the scale factor for this enlargement? Complete shape Q. What are the co ordinates of the centre of enlargement? Enlarge shape P by a scale factor of ½ about (3,14) to give shape R. 16 14 12 10 8 6 4 2 5 15 13 11 9 7 3 1 18 17 19 the scale factor from P to Q is 2 R Q the centre of enlargement is at (0,0) P © T Madas
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 5 4 3 2 1 -1 -2 -3 -4 -5 Exam Question © T Madas
P Enlarge this triangle by a scale factor of 1½, about P 5 4 3 2 1 -1 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 5 4 3 2 1 -1 -2 -3 -4 -5 Enlarge this triangle by a scale factor of 1½, about P P © T Madas
© T Madas
Q P Shape P is enlarged to give shape Q. One of the sides of shape Q has been drawn on the grid. State the scale factor for this enlargement. Complete shape Q on the grid. A B A ¢ B ¢ Q P C ¢ D ¢ C D E ¢ The scale factor is ½ E © T Madas
© T Madas