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Enlargements 1
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ENLARGEMENTS
B. DRAWING ENLARGEMENTS
A. SCALE FACTORS
C. CENTRES OF ENLARGEMENT
D. OTHER SCALE FACTORS
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Enlargements
Odd One Out A1 A2 A3 A4 A5 A6
Guess the scale factor B1 B2 B3
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.
DRAWING ENLARGMENTS: This section demonstrates how enlargements are drawn from a given center of enlargement and a scale factor.
General Examples C1 C2 C3
C4 C5 Examples on Grids
A number of practice exercises where the idea of “scale factor“ is explored.
F1 F2 F3
E1 E2 E3 Fractional Enlargements
Negative Enlargements
FINDING THE CENTRE OF ENLARGEMENT: How lines are drawn back through corresponding points to give the centre of enlargement.
D1 D2 D3 D4 D5 Example 5 Spelt out!
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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?A1
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A x 2
B
C x 2
x 3
Odd One Out?A1
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A
B
C
Odd One Out?A2
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A x 2
B
C
x 2
x 3
Odd One Out?A2
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A
B
C
Odd One Out?A3
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A x 1.5
B
C x 1.5
x 2
Odd One Out?A3
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A
B
C
Odd One Out?A4
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A x 3
B
C
x 3
x 2
Odd One Out?A4
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A
B
C
Odd One Out?A5
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A
B
C
x 1.5
x 2
x 2
Odd One Out?A5
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A
B
C
Odd One Out?A6
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A x 2
B
C x 2
x 3
Odd One Out?A6
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Guess the Scale Factor?
A B C Dx 2 x 4x 3 x 5
B1
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Guess the Scale Factor?
x 3B C Dx 2 x 4 x 5
A
B1
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Guess the Scale Factor?
B C Dx 2 x 4x 3 x 5
A
B2
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x 2A C Dx 3 x 4 x 5
B
Guess the Scale Factor?B2
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Guess the Scale Factor?
Need to be accurate here!!!
B C Dx 1.25 x 2x 1.5 x 2.25A
B3
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Guess the Scale Factor?
Need to be accurate here!!!
BCx 1.25 x 2x 1.5A x 2.25DB
B3
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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 + 2Multiply the length of each line by 2
Can you see the outline of the IMAGE?
C1
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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?
C2
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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
lengths by 2Note the outline
of the IMAGE
C3
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0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Enlarge this shape by ...
Scale factor + 2
Centre of Enlargement
( 1 , 2 )
• Multiply the length of each line by 2
• Can you see the outline of the image?
Drawing EnlargementsC4
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0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Enlarge this shape by ...
Scale factor + 2
Centre of Enlargement
( 9 , 10 )
• Multiply the length of each line by 2
• Can you see the outline of the image?
Drawing EnlargementsC5
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Finding Centres of Enlargement
xCentre
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0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
The Shape
The Image
Now draw the lines back to the ...CENTRE OF ENLARGEMENT
x
Find the Centre of Enlargement?
( 1 , 2 ) SCALE FACTOR + 2
D1
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0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
The Shape
The Image
Now draw the lines back to the ...CENTRE OF ENLARGEMENT
x
Find the Centre of Enlargement?
( 1 , 0 ) SCALE FACTOR + 3
D2
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0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
The Shape
The Image
Now draw the lines back to the ...CENTRE OF ENLARGEMENT
x
Find the Centre of Enlargement?
( 5 , 0 ) SCALE FACTOR + 3
D3
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0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
The Shape
The Image
Now draw the lines back to the ...CENTRE OF ENLARGEMENT
x
Find the Centre of Enlargement?
( 8 , 1 ) SCALE FACTOR + 2
D4
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0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
The Shape
The Image
Now draw the lines back to the ...CENTRE OF ENLARGEMENT
x
Find the Centre of Enlargement?
( 7 , 1 ) SCALE FACTOR + 0.5
D5
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0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
WATCH THE
ORDER CAREFULLY
The Shape
The Image
x
Why + 0.5 and not + 2 ???
( 7 , 1 ) SCALE FACTOR + 0.5
D5
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Fractional and Negative Enlargements
x 0.5
E
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Fractional Enlargement 1
x divide all lengths by 3 13
E1
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Fractional Enlargement 2
x multiply all lengths by 0.75 34
E2
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Fractional Enlargement 3
x multiply all lengths by 0.6 35
E3
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Negative Enlargement 1
x -1 multiply all lengths by 1 and draw in the opposite (negative) direction.
E4
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Negative Enlargement 2
x -1 multiply all lengths by 1 and draw in the opposite (negative) direction.
E5
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Negative Enlargement 3
x -2 multiply all lengths by 2 and draw in the opposite (negative) direction.
E6