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Year 9 Enlargement

Year 9 Enlargement. Dr J Frost (jfrost@tiffin.kingston.sch.uk). Last modified: 2 nd November 2014. 8 6 4 2 -2 -4 -6. -10 -8 -6 -4 -2 2 4 6 8 10. ROTATE

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Year 9 Enlargement

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  1. Year 9 Enlargement Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 2nd November 2014

  2. 8 6 4 2 -2 -4 -6 -10 -8 -6 -4 -2 2 4 6 8 10 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

  3. y Starter 4 Describe the transformations that resulted in the 3 images. (If you finish, can you describe the transformation resulting in Image A using only reflections?) 3 Object 2 1 Image A x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 Image B Image C -2 -3 -4

  4. y Describing an Enlargement 4 It’s becoming 2 times as wide. 3 Image It’s becoming 4 times in size in terms of area. 2 1 Object x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 It’s being enlarged about some point. -2 -3 Clearly this shape is being ‘enlarged’ in some way. What two things might describe such a transformation? Click to Start Bromanimation -4

  5. y Describing an Enlargement 4 3 ...by a scale factor of 2. Image 2 1 Object x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 An enlargement about the point (-5, -1) -2 -3 -4

  6. y Example 1 4 Describe enlargement from A to B. 3 B 2 The centre of enlargement. A 1 x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 The distance from the centre is being tripled, so we have enlargement by a scale factor of 3. -2 -3 “Enlargement about the point (-3, 1) by a scale factor of 3.” -4

  7. y Example 2 4 Describe enlargement from A to B. 3 A 2 B 1 x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 -3 “Enlargement about the point (-3, 1) by a scale factor of .” -4

  8. y Test Your Understanding 4 Describe enlargement from A to B. 3 2 B 1 x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 A -2 -3 -4 “Enlargement about the point (-2, -3) by a scale factor of .”

  9. y Drawing an Enlargement 4 Enlarge the shape by a scale factor of 2 about the point (0,-2) 3 2 1 Image x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 Object -1 -2 -3 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 -4

  10. y Example 4 4 Enlarge the shape by a scale factor of about the point (-3,-1) 3 2 1 Image x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 Object -2 -3 -4

  11. y Test Your Understanding 4 3 2 1 Object x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 Image -2 -3 -4 Enlarge the shape by a scale factor of about the point (1,3)

  12. y Negative Enlargement 4 Enlarge the shape by a scale factor of -1 about the point (0,2) 3 2 Image 1 Object x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 -3 -4 Bro Tip: When the scale factor is negative, the principle is exactly the same. Any ‘negative distances’ go in the opposite direction.

  13. y Test Your Understanding 4 3 2 1 Object Image x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 -3 Enlarge the shape by a scale factor of -2 about the point (1,1) -4

  14. y Test Your Understanding 4 3 2 Image 1 Object x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 -3 Enlarge the shape by a scale factor of -0.5 about the point (0,2) -4

  15. y Test Your Understanding 4 3 2 1 Object Image x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 -3 -4 Enlarge the shape by a scale factor of -1.5 about the point (1,1)

  16. Worksheet Time

  17. Answers

  18. Answers

  19. Answers Enlargement of scale factor 2 about the origin. ?

  20. Answers B

  21. Answers

  22. Answers Enlargement by a scale factor of 3 about the origin. ?

  23. Answers ? Enlargement of scale factor 3 about the origin.

  24. y Recap 4 3 2 Object 1 Image x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 Enlarge the shape by a scale of about the point . Point A maps to . Point B maps to Point C maps to -3 ? ? -4 ?

  25. y Recap 4 3 2 Object 1 x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 Image -1 -2 Enlarge the shape by a scale of about the point . Point A maps to . Point B maps to Point C maps to -3 ? ? -4 ?

  26. Year 9 Combined Transformations Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 5th October 2013

  27. y Starter 4 (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? 3 Final Image Object 2 1 Image after rotation x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 -3 -4

  28. y 4 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? 3 Object 2 1 x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 Final Image -2 -3 -4

  29. y 4 Sketch the following in your books. List the sequence of two transformations which results in the image. 3 2 1 Object x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 Image -2 -3 -4

  30. y 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. 4 3 2 Object 1 x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 -3 *Although to keep things simple, the line of reflection must be in the form x = c, y = c, y = x or y = -x -4

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