Year 9 Enlargement Dr J Frost (jfrosttiffin.kingston.sch.uk) Last modified: 2nd November 2014 ROTATE Warning: Pressing this button may result in death or loss of limbs. REFLECT Warning: Pressing this button may result in bowel problems.
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Presentation Transcript
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Year 9 Enlargement Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 2nd November 2014<br>
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ROTATE
Warning: Pressing this button may result in death or loss of limbs. REFLECT
Warning: Pressing this button may result in bowel problems. TRANSLATE
Warning: Do not press if you are pregnant or suffer from a heart condition. ENLARGE
Warning: Pressing this button may result in loss of girlfriend. N<br>
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x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 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?)<br>
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x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 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?<br>
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x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 Object Image ...by a scale factor of 2. An enlargement about the point (-5, -1)<br>
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x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 A The 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 Describe enlargement from A to B.<br>
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x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 Describe enlargement from A to B. B A<br>
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x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 Describe enlargement from A to B. B A<br>
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x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 Object Enlarge the shape by a scale factor of 2 about the point (0,-2) 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<br>
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 Object Enlarge the shape by a scale factor of -1 about the point (0,2) Image Bro Tip: When the scale factor is negative, the principle is exactly the same. Any ‘negative distances’ go in the opposite direction.<br>
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x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 Enlarge the shape by a scale factor of -2 about the point (1,1) Object Image<br>
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x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 Object Enlarge the shape by a scale factor of -0.5 about the point (0,2) Image<br>
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x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 Enlarge the shape by a scale factor of -1.5 about the point (1,1) Object Image<br>
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Enlargement of scale factor 2 about the origin. ?<br>
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B<br>
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Enlargement by a scale factor of 3 about the origin. ?<br>
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Enlargement of scale factor 3 about the origin. ?<br>
Year 9 Combined Transformations Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 5th October 2013<br>
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x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 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?<br>
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x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 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?<br>
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x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 Object Image Sketch the following in your books.
List the sequence of two transformations which results in the image.<br>
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x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 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<br>
