© T Madas
Enlarge this rectangle by a scale factor of 2
about the marked centre of enlargement
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?
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?
C
© T Madas
Enlarge this rectangle by a scale factor of 2
about the marked centre of enlargement
C
0
I
Can you see where
the rest of the shape
will be?
© T Madas
Why is the centre of enlargement important?
C
0
© T Madas
Why is the centre of enlargement important?
Can you see where
the rest of the shape
will be?
C
0
© T Madas
Why is the centre of enlargement important?
Can you see where
the rest of the shape
will be?
C
0
© T Madas
Why is the centre of enlargement important?
Can you see where
the rest of the shape
will be?
C
0
© T Madas
Why is the centre of enlargement important?
To enlarge a shape you need:
C
A Scale Factor (Size)
Centre of Enlargement (Position)
0
I
© T Madas
Enlarge this shape by a scale factor of 3 about the
marked centre of enlargement
C
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
C
© T Madas
Enlarge this shape by a scale factor of 3 about the
marked centre of enlargement
C
© T Madas
Enlarge this shape by a scale factor of 3 about the
marked centre of enlargement
C
© T Madas
Enlarge this shape by a scale factor of 3 about the
marked centre of enlargement
C
O
I
© T Madas
The Different Positions
of the
Centre of Enlargement
© T Madas
The centre of enlargement can
lie on a corner of the shape
x4
x3
x2
C
© T Madas
The centre of enlargement
can lie on a side of the shape
C
x2
x3
© T Madas
The centre of enlargement
can lie inside the shape
C
x2
x3
© 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
x3
C
6
12
© T Madas
Finding The
Centre of Enlargement
© T Madas
Where is the centre of enlargement?
C
O
I
© T Madas
Where is the centre of enlargement?
I
O
C
© T Madas
Scale Factor Pairs
© T Madas
What is the scale factor from A to B?
x2
What is the scale factor from B to A?
x½
C
A
B
© T Madas
What is the scale factor
from A to B?
x3
What is the scale factor
from B to A?
1
x 3
B
A
C
© T Madas
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
© T Madas
Negative
Scale
Factors
© T Madas
What is the meaning of a
negative scale factor?
© T Madas
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?
© T Madas
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
© T Madas
Enlarge object A by a scale factor of -1
-2
C
B
A
© T Madas
Enlarge object A by a scale factor of -1
-2
C
A
B
What is the scale factor from B to A? –
1
2
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
-2
1
-1
2
3
4
5
6
7
-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
P
6
5
4
3
2
1
-7
-6
-5
-4
-3
-2
1
-1
2
3
4
5
6
-1
-2
-3
-4
-5
© T Madas
© T Madas
Enlarge the trapezium shown below by a scale factor of
½, with centre of enlargement the origin.
10
9
8
7
6
5
4
3
2
1
-11 -10
-9
-8
-7
-6
-5
-4
-3
-2
1
-1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
-1
-2
-3
-4
-5
-6
-7
-8
© T Madas
© T Madas
Shape P is enlarged to give shape Q.
One side of shape Q is drawn for you.
1.
2.
3.
4.
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 17
scale factor of ½ 16
about (3,14) to give 15
14
shape R.
13
12
the scale factor from P
to Q is 2
the centre of enlargement
is at (0,0)
11
R
10
9
Q
8
7
6
P
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19
© T Madas
Enlarge this triangle by a scale
factor of 1½,
5
about P
4
3
2
1
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-1
-2
-3
P
-4
-5
© 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.
2.
State the scale factor for this enlargement.
Complete shape Q on the grid.
B
A
B A
Q
P
C
D
C
D
E
The scale factor is ½
E
© T Madas