Transcript Centre of enlargement

Centre of enlargement
Centre of enlargement
• OBJECTIVE
• Understand centre of
enlargement and
scale factors,
negative and positive
and less than 1
• SUCCESS CRITERIA
• Identify centre of
enlargement
• Identify scale factor
• Enlargement greater
than 1
• Enlargement less
than 1
• Enlargements that are
negative
Key words
• Centre of
enlargement
• Scale factor
• Corresponding
• Positive
• Negative
• Less than
• Greater than
•
•
•
•
•
•
•
•
Fraction
Line
Extend
Rotate
Multiply
Coordinates
Vertices
Enlargement
Centre of enlargement
• The centre of enlargement gives the position
from which the enlargement will take place
• When we blow up a balloon the centre of
enlargement would be from the spout where the
gas was entering
• If we shine a light at an object so that its shadow
appeared on a wall. The shadow would be an
enlargement of the original figure and the light
source would be the centre of enlargement.
Centre of enlargement
11
9
7
Corresponding vertices
A
5
3
Centre of enlargement (3, 3)
1
1
3
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9
11
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15
17
19
Centre of enlargement – positive
scale factor greater than 1
• When the scale factor is positive then the
enlargement appears on the same side of
the centre of enlargement as the original
shape.
• The drawing will show centre of
enlargement, original shape and enlarged
shape in that order.
Centre of enlargement – positive
scale factor greater than 1
• Draw lines from the centre of enlargement
through the vertices of the original shape
• The length from the centre of enlargement
to the original shape is increased by the
scale factor to determine the vertices of
the enlarged shape
• The position of the new shape is always
measured from the centre of enlargement
Centre of enlargement – positive scale factor
The length of the line
from the centre of
enlargement to the
original shape is
increased by the scale
factor
11
9
7
A
5
This shows shape A
enlarged by a scale
factor of 2 about
the centre of
enlargement (4, 3)
3
1
1
3
5
7
9
11
13
15
17
19
Centre of enlargement – positive scale factor
11
9
7
A
5
Enlarge this shape by
a scale factor of 3
about the centre of
enlargement (3, 3)
3
1
1
3
5
7
9
11
13
15
17
19
Centre of enlargement – positive scale factor
11
9
The lines from the
centre of enlargement to
the original shape are
increased by a scale
factor of 3 to provide
the position of the
enlarged shape
7
A
5
3
1
1
3
5
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Centre of enlargement – exercise 1
enlarge both shapes by a scale factor of 3
about the centres of enlargement indicated
11
9
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3
1
1
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Centre of enlargement – exercise 1
answer
11
9
7
5
3
1
1
3
5
7
9
11
13
15
17
19
Enlarge both shapes by a scale factor of 2
about the centres of enlargement indicated
11
9
7
5
3
1
1
3
5
7
9
11
13
15
17
19
Enlarge both shapes by a scale factor of 2
about the centres of enlargement indicated
11
9
7
5
3
1
1
3
5
7
9
11
13
15
17
19
Enlarge both shapes by a scale factor of 3
about the centres of enlargement indicated
11
9
7
5
3
1
1
3
5
7
9
11
13
15
17
19
Enlarge both shapes by a scale factor of 3
about the centres of enlargement indicated
11
9
7
5
3
1
1
3
5
7
9
11
13
15
17
19
Centre of enlargement – negative
scale factor
• When the scale factor is negative then the
enlargement appears on the opposite side
of the centre of enlargement as the
original shape.
• The drawing will show original shape,
centre of enlargement and enlarged shape
in that order.
Centre of enlargement – negative
scale factor
• Draw lines from the vertices of the original
shape through the centre of enlargement
• The length from the centre of enlargement
to the original shape is increased by the
scale factor to determine the vertices of
the enlarged shape
• The position of the new shape is always
measured from the centre of enlargement
Centre of enlargement – negative scale factor
11
9
A
7
This shows shape A
enlarged by a scale
factor of -2 about
the centre of
enlargement (10, 7)
5
3
1
1
3
5
7
9
11
13
15
17
19
Centre of enlargement – negative scale factor
11
9
7
A
5
Enlarge this shape by
a scale factor of -3
about the centre of
enlargement (3, 3)
3
1
1
3
5
7
9
11
13
15
17
19
Centre of enlargement – negative scale factor
The length of the line
from the C of E to the
enlargement is 3 times
the length of the line
from the shape to the C
of E
11
9
7
A
5
Enlarge this shape by
a scale factor of -3
about the centre of
enlargement (3, 3)
3
1
1
3
5
7
9
11
13
15
17
19
Centre of enlargement – scale factor of -1
An enlargement by a scale factor of -1 is the same as a
rotation of 1800 about the same point
11
9
7
This shows shape A
enlarged by a scale
factor of -1 about
the centre of
enlargement (10, 7)
A
This is the same as a
rotation of 1800
about centre of
rotation (10, 7)
5
3
1
1
3
5
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Centre of enlargement – exercise 2
enlarge both shapes by a scale factor of -2
about the centres of enlargement indicated
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9
7
5
3
1
1
3
5
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Centre of enlargement – exercise 2
answer
11
9
7
5
3
1
1
3
5
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9
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13
15
17
19
Enlarge each shape by a scale factor of -3
11
9
7
A
5
3
1
1
3
5
7
9
11
13
15
17
19
Enlarge each shape by a scale factor of -3
11
9
7
A
5
3
1
1
3
5
7
9
11
13
15
17
19
Centre of enlargement – Positive
scale factor less than 1
• When the scale factor is less than 1 then
the enlargement appears between the
centre of enlargement and the original
shape.
• The drawing will show original shape,
enlarged shape and centre of enlargement
in that order.
• We still call it an enlargement although it is
smaller.
Centre of enlargement – Positive
scale factor less than 1
• Draw lines from the vertices of the original
shape to the centre of enlargement.
• The length from the centre of enlargement
to the original shape is multiplied by the
scale factor to determine the vertices of
the enlarged shape.
• The position of the new shape is always
measured from the centre of enlargement.
Centre of enlargement – scale factor less than 1
11
9
A
7
This shows shape A
enlarged by a scale
factor of ½ about
the centre of
enlargement (4, 3)
5
3
1
1
3
5
7
9
11
13
15
17
19
Centre of enlargement – scale factor less than
1
11
9
Enlarge the shape by a
scale factor of 1/3 about
the centre of
enlargement (3, 3)
7
A
5
3
1
1
3
5
7
9
11
13
15
17
19
Centre of enlargement – scale factor less than
1
11
9
Enlarge the shape by a
scale factor of 1/3 about
the centre of
enlargement (3, 3)
7
A
5
3
1
1
3
5
7
9
11
13
15
17
19
Centre of enlargement – scale factor less than 1
enlarge both shapes by a scale factor of 1/3 about the Centre
of Enlargements indicated
11
9
7
5
3
1
1
3
5
7
9
11
13
15
17
19
Centre of enlargement – scale factor less than 1
enlarge both shapes by a scale factor of 1/3 about the Centre
of Enlargements indicated
11
9
7
5
3
1
1
3
5
7
9
11
13
15
17
19
Finding the Centre of enlargement
• To find the centre of enlargement we must
draw lines through the corresponding
vertices of both shapes.
• Where the lines cross is the centre of
enlargement
Find Centre of enlargement
11
This shows that the
centre of
enlargement is (1, 1)
9
7
This is found by
drawing lines through
the corresponding
vertices of the
shapes.
5
3
1
1
3
5
7
9
11
13
15
17
19
Finding the Centre of enlargement
Find the centre of
enlargement.
11
9
7
A
5
3
1
1
3
5
7
9
11
13
15
17
19
Finding the Centre of enlargement
Find the centre of
enlargement.
11
9
7
A
5
3
1
1
3
5
7
9
11
13
15
17
19
Find the centre of enlargement - exercise
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Find the centre of enlargement – answer
(2, 2) and (19, 1)
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1
1
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Finding the scale factor
• To find the scale factor we divide a length
on the enlarged shape by a corresponding
length on the original shape
• Scale factor = enlarged length ÷ original length
Find the scale factor of enlargement
The scale factor from
the smaller shape to the
larger shape is 3
11
9
This is found by
comparing the lengths
of the corresponding
sides.
7
5
3
2 × scale factor = 6
Scale factor = 6 ÷ 2 = 3
1
1
3
5
7
9
11
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19
Find the scale factor of enlargement for these shapes exercise
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9
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3
1
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Find the scale factor of enlargement for these shapes
answer
2 and 3
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9
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3
1
1
3
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Centre of enlargement
Enlarge shape A about (1, 2) by a scale factor of
a)
3
b)
-4
c)
-1
4
A
2
-10
-8
-6
-4
-2
2
-2
-4
-6
4
6
8
10
Centre of enlargement
enlarge shape A about (1, 2) by a scale factor of
a)
3
b)
-4
c)
-1
4
a) 2
A
2
c) -1
-10
-8
b) -4
-6
-4
-2
2
-2
-4
-6
4
6
8
10
Centre of enlargement - review
•
•
•
•
•
Identify centre of enlargement
Identify scale factor
Enlargement greater than 1
Enlargement less than 1
Enlargements that are negative
Complete the paragraph using the words below
The centre of enlargement is a point from which a shape is enlarged.
Positive scale factors --------- --------- one produce shapes that are
larger than the original shape so that the centre of enlargement,
original shape and --------- shape appear in that order. Negative
--------- --------- less than minus one produce enlarged shapes that appear
rotated. Scale factors less than one produce smaller enlargements
although we still call them enlargements. To find the --------- -- -------- we draw lines through the corresponding --------- of the shapes. The
coordinates where these --------- meet is the centre of enlargement.
Centre of enlargement, Scale factors, Corresponding, Positive, Negative,
Less than, Greater than, Fraction, Lines, Extend, Rotate, Multiply,
Coordinates, Vertices, Enlarged
Complete the paragraph using the words below
The centre of enlargement is a point from which a shape is enlarged.
Positive scale factors greater than one produce shapes that are larger
than the original shape so that the centre of enlargement, original
shape and enlarged shape appear in that order. Negative scale factors
less than minus one produce enlarged shapes that appear rotated.
Scale factors less than one produce smaller enlargements although we
still call them enlargements. To find the centre of enlargement we
draw lines through the corresponding vertices of the shapes. The
coordinates where these lines meet is the centre of enlargement.
Centre of enlargement, Scale factors, Corresponding, Positive, Negative,
Less than, Greater than, Fraction, Lines, Extend, Rotate, Multiply,
Coordinates, Vertices, Enlarged