Transcript 14_Enlargement_1
Enlargements 1
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ENLARGEMENTS
A. SCALE FACTORS B. DRAWING ENLARGEMENTS C. CENTRES OF ENLARGEMENT D. OTHER SCALE FACTORS
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Enlargements
Practice exercises exploring the idea of scale factor. Some of the numbers involved are deliberately tricky in order to generate discussion and “hands on” measurement of corresponding lengths.
Odd One Out Guess the scale factor
DRAWING ENLARGMENTS: This section demonstrates how enlargements are drawn from a given center of enlargement and a scale factor.
General Examples Examples on Grids
FINDING THE CENTRE OF ENLARGEMENT: How lines are drawn back through corresponding points to give the centre of enlargement.
A number of practice exercises where the idea of “scale factor“ is explored.
Fractional Enlargements
Negative Enlargements
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SECTION A
A. BASICS + SCALE FACTORS
x 2 ?
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Odd One Out?
In each of the diagrams
TWO
have been enlarged by the SAME scale factor.
Look carefully at the lengths on the diagrams and ....
Spot the
ODD ONE OUT?
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A B C
Odd One Out?
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A B C
Odd One Out?
x 2
x 3
x 2
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A B C
Odd One Out?
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A B C
Odd One Out?
x 2 x 2
x 3
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A B C
Odd One Out?
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A B C
Odd One Out?
x 1.5
x 2
x 1.5
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A B C
Odd One Out?
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A B C
Odd One Out?
x 3 x 3
x 2
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A B C
Odd One Out?
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A B C
Odd One Out?
x 1.5
x 2 x 2
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A B C
Odd One Out?
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A B C
Odd One Out?
x 2
x 3
x 2
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Guess the Scale Factor?
A
x 2
B
x 3
C
x 4
D
x 5
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Guess the Scale Factor?
A
x 2
B
x 3 C
x 4
D
x 5
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Guess the Scale Factor?
A
x 2
B
x 3
C
x 4
D
x 5
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Guess the Scale Factor?
A
x 2 B
x 3
C
x 4
D
x 5
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Guess the Scale Factor?
Need to be accurate here!!!
A
x 1.25
B
x 1.5
C
x 2
D
x 2.25
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Guess the Scale Factor?
Need to be accurate here!!!
A
x 1.25
B
x 1.5
C
x 2
x 2.25
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SECTION 2
Drawing enlargements
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Drawing Enlargements
•
Start with a point and a shape
•
Draw lines to each point on the shape Scale Factor + 2 Multiply the length of each line by 2 Can you see the outline of the IMAGE?
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Drawing Enlargements
•
Start with a point and a shape
•
Draw lines to each point on the shape Scale Factor + 3 Multiply the length of each line by 3 Can you see the outline of the IMAGE?
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Drawing Enlargements
•
Start with a point and a shape
•
Draw lines to each point on the shape Note the outline of the IMAGE Scale Factor + 2 Multiply the lengths by 2
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Drawing Enlargements Enlarge this shape by ...
Scale factor + 2 Centre of Enlargement ( 1 , 2 )
10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 •
Multiply the length of each line by 2
4 5 6 7 •
Can you see the outline of the image?
8 9 10
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Drawing Enlargements Enlarge this shape by ...
Scale factor + 2 Centre of Enlargement ( 9 , 10 )
10 9 5 4 3 2 8 7 6 1 0 0 1 2 3 4 5 6 7 8 9 10 •
Multiply the length of each line by 2
•
Can you see the outline of the image?
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Finding Centres of Enlargement Centre x
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Find the Centre of Enlargement?
The Shape The Image
Now draw the lines back to the ...
CENTRE OF ENLARGEMENT
10 9 8 7 6 5 4 3 2 1 0 0
x
1 2 3 4 5 6 7 8 9 10
( 1 , 2 ) SCALE FACTOR + 2
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Find the Centre of Enlargement?
The Shape The Image
Now draw the lines back to the ...
CENTRE OF ENLARGEMENT
6 5 4 3 2 1 0 10 9 8 7 0
x
1 2 3 4 5 6 7 8 9 10
( 1 , 0 ) SCALE FACTOR + 3
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Find the Centre of Enlargement?
The Shape The Image
Now draw the lines back to the ...
CENTRE OF ENLARGEMENT
10 9 8 7 6 5 4 3 2 1 0 0 1 2
( 5 , 0 )
3 4
x
5 6 7 8 9 10
SCALE FACTOR + 3
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Find the Centre of Enlargement?
The Shape The Image
Now draw the lines back to the ...
CENTRE OF ENLARGEMENT
10 9 8 7 6 5 4 3 2 1 0 0 1 2
( 8 , 1 )
3 4 5 6 7
x
8 9 10
SCALE FACTOR + 2
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Find the Centre of Enlargement?
The Shape The Image
Now draw the lines back to the ...
CENTRE OF ENLARGEMENT
10 9 8 7 6 5 4 3 2 1
x
0 0 1 2
( 7 , 1 )
3 4 5 6 7 8 9 10
SCALE FACTOR + 0.5
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Why + 0.5 and not + 2 ???
WATCH THE
ORDER
CAREFULLY
The Shape The Image 10 9 3 2 1 0 8 7 6 5 4 0 1 2
x
3 4 5 6 7 8 9 10
( 7 , 1 )
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Fractional and Negative Enlargements x 0.5
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Fractional Enlargement 1
1 x divide all lengths by 3 3
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Fractional Enlargement 2
3 x multiply all lengths by 0.75 4
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Fractional Enlargement 3
3 x multiply all lengths by 0.6 5
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Negative Enlargement 1
x -1 multiply all lengths by 1 and draw in the opposite (negative) direction.
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Negative Enlargement 2
x -1 multiply all lengths by 1 and draw in the opposite (negative) direction.
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Negative Enlargement 3
x -2 multiply all lengths by 2 and draw in the opposite (negative) direction.
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