© t madas. enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement c 0...
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© T Madas
© T Madas
Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement
C0
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Centre of Enlargement
© T Madas
Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement
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Can you see where the rest of the shape will be?
© T Madas
Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement
C
Can you see where the rest of the shape will be?
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© T Madas
Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement
C 0I
0 1 2 3
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Can you see where the rest of the shape will be?
© T Madas
Why is the centre of enlargement important?
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© T Madas
Why is the centre of enlargement important?
C0 1 2
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Can you see where the rest of the shape will be?
© T Madas
Why is the centre of enlargement important?
C
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Can you see where the rest of the shape will be?
© T Madas
0
Why is the centre of enlargement important?
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Can you see where the rest of the shape will be?
© T Madas
Why is the centre of enlargement important?
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To enlarge a shape you need:
A Scale Factor
Centre of Enlargement
(Size)
(Position)
© T Madas
Enlarge this shape by a scale factor of 3 about the marked centre of enlargement
C
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Can you see where the rest of the shape will be?
© T Madas
Enlarge this shape by a scale factor of 3 about the marked centre of enlargement
C0
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© T Madas
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
© T Madas
Enlarge this shape by a scale factor of 3 about the marked centre of enlargement
C0
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
C OI
© T Madas
The Different Positionsof the
Centre of Enlargement
© T Madas
The centre of enlargement can lie on a corner of the shape
C
x 4
x 3
x 2
© T Madas
C
The centre of enlargement can lie on a side of the shape
x 2x 3
© T Madas
C
The centre of enlargement can lie inside the shape
x 2x 3
© T Madas
Formal Enlargementon square paper
© T Madas
If you are using square paper you can use the following method to enlarge:
C
Scale factor 3
© T Madas
If you are using square paper you can use the following method to enlarge:
24
x 36
12
C
Scale factor 3
© T Madas
Finding TheCentre of Enlargement
© T Madas
I
O
Where is the centre of enlargement?
C
© T Madas
Where is the centre of enlargement?
CO
I
© T Madas
Scale Factor Pairs
© T Madas
C BA
x 2What is the scale factor from A to B?
x ½What is the scale factor from B to A?
© T Madas
C
B
A
What is the scale factor from A to B?
What is the scale factor from B to A?x 1
3
x 3
© T Madas
What is the scale factor from A to B?
What is the scale factor from B to A?x 2
3
BAC
x 32
The scale factors which transform object to image and vice versa are always reciprocals of each other
© T Madas
NegativeScale
Factors
© T Madas
What is the meaning of a negative scale factor?
© T Madas
AB
C
+ve-ve
Enlarge object A by a scale factor of -1
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
AB
C
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
AB
C
Enlarge object A by a scale factor of -1
-2
© T Madas
AC
Enlarge object A by a scale factor of -1
-2
B
What is the scale factor from B to A?
What combination of transformations would have produced the same result from A to B?
– 12
© T Madas
© T Madas
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-2 2 4 6-1 3 5 71
Enlarge the triangle shown below by a scale factor of 3, with centre of enlargement the origin.
© T Madas
© T Madas
Enlarge the triangle shown below by a scale factor of 2½, with centre of enlargement the point P.
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P
© T Madas
© T Madas
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5 101 2 3 4 6 7 8 9 11 12 13 14 15-5-10 -1-2-3-4-6-7-8-9-11
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Enlarge the trapezium shown below by a scale factor of ½, with centre of enlargement the origin.
© T Madas
© T Madas
4. Enlarge shape P by a scale factor of ½ about (3,14) to give shape R.
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Shape P is enlarged to give shape Q.One side of shape Q is drawn for you.
1. What is the scale factor for this enlargement?2. Complete shape Q. 3. What are the co ordinates of the centre of enlargement?
P
Qthe scale factor from P to Q is2
the centre of enlargement is at (0,0)
R
© T Madas
Exam Question-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
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-5
© T Madas
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
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Enlarge this triangle by a scale factor of 1½, about P
P
© T Madas
© T Madas
Shape P is enlarged to give shape Q.
One of the sides of shape Q has been drawn on the grid.
1. State the scale factor for this enlargement.
2. Complete shape Q on the grid.
QP
The scale factor is½
A AB
C
D
E
B
CD
E
© T Madas
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