Enlargement
Objectives:
F Grade
Give a scale factor of an enlarged shape
E Grade
Enlarge a shape by a positive scale factor
Find the measurements of the dimensions
of an enlarged shape
D Grade
Enlarge a shape by a positive scale factor
from a given centre
C Grade
Find the centre of enlargement
Enlargement
A 2-D shape can be made larger by a given amount
This is called the Scale Factor
w
object
2w
image
l
2l
Notice how the sides
of the image are twice
that of the object
This is an enlargement
scale factor 2
If the length the sides was increased to be 3 times as long
the scale factor would be 3
Enlargement
Objects can be enlarged using the scale factor to extend the length
of the sides, because it is the sides that are increased it is called the
linear scale factor.
As was seen by finding the length of the image side by:
image line length = object line length × scale factor
similarly
linear scale factor = object line length
image line length
This name is only important when the area and / or volume are
part of the consideration for enlargement.
Now do these:
Enlargement
Enlarge these shapes alongside by a scale factor of 2
1.
3.
2.
Enlarge these shapes below by a scale factor of 3
4.
5.
Enlargement
Identify the scale factor used to enlarge these shapes
6.
8.
7.
scale factor 2.5
scale factor 3
scale factor 4
Enlargement
Normally an enlargement is required given a centre of enlargement.
Using the centre of enlargement locates the image.
Draw construction lines from the centre of enlargement CoE
through the vertices of the object. Ray Lines
Using a scale factor 2 the distance from the CoE to the image
vertices is 2 times the distance from the CoE to the object vertices.
CoE
2 squares right
1 square down
object
x
5 squares right
1 square down
x
Scale Factor 2
Distance from CoE
4 squares right
2 squares down
Scale Factor 2
Distance from CoE
10 squares right
2 squares down
2 squares right
3 squares down
x
This gives us enough information to draw the image
Scale Factor 2
Distance from CoE
4 squares right
6 squares down
Enlargement
Repeat this to see the effect of a scale factor 3
5 squares right
1 square down
CoE
object
Scale Factor 3
Distance from CoE
15 squares right
3 squares down
2 squares right
1 square down
Scale Factor 3
Distance from CoE
6 squares right
3 squares down
2 squares right
3 squares down
Scale Factor 3
Distance from CoE
6 squares right
9 squares down
x
x
x
This gives us enough information to draw the image
Enlargement
The position of the centre of enlargement relative to the object makes a
difference as to where the enlarged image is positioned.
CoE
CoE
CoE
CoE
CoE
CoECoE
CoECoE
Moving
the
centre
of
enlargement
away
fromthe
the
object
moves
Movingthe
thecentre
centreof
ofenlargement
enlargementdown
up moves
image
down
Moving
moves
the
image
up the image further
away in the opposite direction
Enlargement
Find the coordinates of the centre of enlargement by drawing the ray lines
-10
-9 -8 -7 -6
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
-5 -4 -3 -2 -1 0
-1
-2
1
2
3
4
5 6
7
8
9 10
-10
-9 -8 -7 -6
-5 -4 -3 -2 -1 0
-1
-2
-3
-3
-4
-5
-4
-5
-6
-6
-7
-7
-8
-8
-9
-10
-9
-10
1
2
3
4
5 6
7
8
9 10
6.
4.
1.
Enlargement
7.
Identify the scale factor used to enlarge these shapes
5.
Enlarge these shapes below by a scale factor of 3
2.
Enlarge these shapes alongside by a scale factor of 2
Worksheet 1
8.
3.
Enlargement
scale factor
3
scale factor 2
2.
4.
scale factor 3
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
-1
-2
-5
-6
-7
-8
-9
-10
-5
-6
-7
-8
-9
-10
-3
-4
-3
-4
9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
-1
-2
8
3
2
1
3
2
1
5 6 7
4
4
4
6
5
6
5
3
7
7
2
1
0
9
8
1
Cx
10
9
8
1
2
C x
scale factor 2.5
Find the coordinates of the centre of enlargement by drawing the ray lines
C x
3.
C x
1.
Enlarge these shapes using the ray line method and C as the
centre of enlargement
Worksheet 2
3
4
5 6 7
8
9 10