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Enlargement
Objectives:
C Grade
Enlarge a shape by a fractional scale factor
Compare the area of an enlarged shape
with the original shape
Find the centre of enlargement
B Grade
Distinguish between formulae for perimeter, area
and volume by considering dimensions
A Grade
Compare areas and volumes of enlarged shapes
Enlarge a shape by a negative scale factor
Prior knowledge:
Enlarge an object by a positive integer scale factor
using a centre of enlargement and ray lines.
Enlargement
Enlargement is not just for making an object bigger using the scale factor
Objects can be enlarged using any number as a scale factor including
fractions and negative numbers.
Using a scale factor ½ the distance from the CoE to the image
vertices is ½ times the distance from the CoE to the object vertices.
10 squares right
2 squares down
CoE
x
4 squares right
2 squares down
x
x
object
Scale Factor ½
Distance from CoE
2 squares right
1 square down
This gives us enough information to draw the image
Scale Factor ½
Distance from CoE
5 squares right
1 square down
4 squares right
6 squares down
Scale Factor ½
Distance from CoE
2 squares right
3 squares down
Enlargement
Negative scale factors can also be used
A negative scale factor takes the image the opposite side of the
centre of enlargement
Enlarge the object by a scale factor of -2
5
4
3
CoE
2
1
-8
-7
-6
-5
-4
-3
-2
-1
0
-1
-2
-3
-4
-5
1
2
3
4
5
6
7
8
9
Enlargement
Enlarge the object by a scale factor of -3
Notice how the image is upside down from the object
5
4
3
2
1
-8
-7
-6
-5
-4
-3
-2
-1
0
1
-1
-2
-3
-4
-5
CoE
2
3
4
5
6
7
8
9
Enlargement
In each case object A has been enlarged to image B
Find the scale factor and centre of enlargement for
A
A
B
B
A
B
Scale Factor ½
Scale Factor -1
A
B
Worksheet 3
Enlargement
In each case object A has been enlarged to image B
Find the scale factor and centre of enlargement for
A
A
B
A
B
B
B
A