Transcript Enlargements

Enlargements
Objectives
To be able to:
Enlarge shapes given a scale factor and
centre of enlargement.
Find centres of enlargement
Scale factors and centres of
enlargement
The size of an enlargement is described by its scale
factor.
For example, a scale factor of 2 means that the new
shape is twice the size of the original.
The position of the enlarged shape depends on the
centre of enlargement.
Enlarge triangle A with a
scale factor of 3 and centre
of enlargement (2,1)
Draw lines from the centre
of enlargement to each
vertex of your shape
y
10
9
8
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6
5
4
3
2
1
Calculate the distance from
the CoE to a vertex and
multiply it by the scale
factor to find its new
position
How do I enlarge a shape?
A’
Repeat for all the
other vertices
A
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Join up your new
points to create your
enlarged shape
x
y
9
8
7
6
5
4
3
2
1
What if the centre of
enlargement is inside the
shape?
Enlarge shape B
with scale factor
2 and centre of
enlargement
(6,6)
B
B’
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x
Enlarge shape C by
scale factor ½ and
centre of
enlargement (10,1)
What about fractional scale
y
factors?
9
8
7
6
5
4
3
2
1
Each vertex on the
enlarged shape is half
the distance from the
CoE than its
corresponding vertex
on the original shape.
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Even though the
shape gets smaller,
it’s still called an
x enlargement.
How do I find the centre of
enlargement?
y
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9
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7
6
5
4
3
2
1
Join up the corresponding
vertices and extend the lines
The point where they all
intersect is your centre of
enlargement
E
CoE = (2,9)
D
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What was the scale
factor of
enlargement?
x