Year 9 Enlargement
Feb 16, 2016
Year 9 Enlargement. Dr J Frost ([email protected]) . Last modified: 5 th October 2013. 8 6 4 2 -2 -4 -6. -10 -8 -6 -4 -2 2 4 6 8 10. ROTATE - PowerPoint PPT Presentation
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-10 -8 -6 -4 -2 2 4 6 8 10
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x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
y4
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Object
Image A
Image B
Image C
Describe the transformations that resulted in the 3 images.
(If you finish, can you describe the transformation resulting in Image A using only reflections?)
Starter
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
y4
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Object
Image
It’s becoming 2 times as wide.
It’s becoming 4 times in size in terms of area.
It’s being enlarged about some point.
Click to Start Bromanimation
Clearly this shape is being ‘enlarged’ in some way. What two things might describe such a transformation?
Describing an Enlargement
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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Object
Image
...by a scale factor of 2.
An enlargement about the point (-5, -1)
Describing an Enlargement
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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AThe centre of enlargement.
The distance from the centre is being tripled, so we have enlargement by a scale factor of 3.
“Enlargement about the point (-3, 1) by a scale factor of 3.”
B
Example 1Describe enlargement from A to B.
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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“Enlargement about the point (-3, 1) by a scale factor of .”
Describe enlargement from A to B.
Example 2
B
A
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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-4“Enlargement about the point (-2, -3) by a scale factor of .”
Describe enlargement from A to B.
Test Your Understanding
B
A
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
y4
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Object
Enlarge the shape by a scale factor of 2 about the point (0,-2)
Drawing an Enlargement
Image
The approach is to take each vertex on the object one at a time, count the squares across and up/down from the centre, and times each by the scale factor
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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Object
Enlarge the shape by a scale factor of about the point (-3,-1)
Example 4
Image
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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Object
Enlarge the shape by a scale factor of about the point (1,3)
Test Your Understanding
Image
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
y4
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Object
Enlarge the shape by a scale factor of -1 about the point (0,2)
Image
Negative Enlargement
Bro Tip: When the scale factor is negative, the principle is exactly the same. Any ‘negative distances’ go in the opposite direction.
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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Enlarge the shape by a scale factor of -2 about the point (1,1)
Object
Image
Test Your Understanding
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
y4
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Object
Enlarge the shape by a scale factor of -0.5 about the point (0,2)
Image
Test Your Understanding
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
y4
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Enlarge the shape by a scale factor of -1.5 about the point (1,1)
Object
Image
Test Your Understanding
Worksheet Time
Answers
Answers
Answers
Enlargement of scale factor 2 about the origin.?
Answers
B
Answers
Answers
Enlargement by a scale factor of 3 about the origin.?
Answers
Enlargement of scale factor 3 about the origin.?
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
y4
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Enlarge the shape by a scale of about the point .
Point A maps to . Point B maps to Point C maps to
Object
Image
Recap
? ??
𝐴
𝐵
𝐶
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
y4
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2
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-1
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Enlarge the shape by a scale of about the point .
Point A maps to . Point B maps to Point C maps to
Object
Image
Recap
? ??
𝐴
𝐵
𝐶
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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Object
Image after rotation
Final Image
(Draw this in your book!)Rotate this object 90 clockwise about the origin, then reflect in the line y = x.How could we have done the same with just one transformation?
Starter
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Object
Final Image
On the same axes, now reflect the object in the y axis followed by the x axis.Again, how could we have done the same with just one transformation?
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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Object
Image
Sketch the following in your books.List the sequence of two transformations which results in the image.
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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Object
Work in pairs:Both sketch the following in your book. Pick a reflection and a rotation of your choice*, sketch the image, then get your neighbour to try and work out the transformations you choose from the image.
*Although to keep things simple, the line of reflection must be in the form x = c, y = c, y = x or y = -x
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