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Enlargements - Ray Method

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Enlargements - Ray Method

  1. 1. Enlargements2.4 Transformation Geometry
  2. 2. Transformation• is when a shape’s size or position is changed or transformed.• the original shape is the OBJECT.• the changed shape is the IMAGE.
  3. 3. Picture
  4. 4. We learn about enlargements!An enlargement changes the SIZE and the POSITION of a shape! To enlarge a shape we need TWO things! 1. A centre of enlargement 2. A scale factor
  5. 5. • When a shape is enlarged, ALL lengths are multiplied by the scale factor (corresponding side lengths are proportional) and all angles remain UNCHANGED.• An example of use is a slide projector.
  6. 6. Slide ProjectorDesign
  7. 7. Better?• In this case, the light bulb is the centre of enlargement!• C. of E. is the point from which the E. is constructed.
  8. 8. Toy Model
  9. 9. Toy Model
  10. 10. Toy Model
  11. 11. The Scale Factor• Is denoted by the letter ‘k’ .• It is the number by which the object is enlarged. http://www.ngfl-cymru.org.uk/vtc/ngfl/maths/echalk/enlargement/intro/enlargementIntro.html
  12. 12. In Action http://www.ngfl-cymru.org.uk/vtc/ngfl/maths/echalk/enlargement/intro/enlargementIntro.html
  13. 13. • Important to note that while enlargements normally enlarge shapes you can also decrease, reduce or make shapes smaller.• For example if k = 1/2 then your shape would be half the original size!• http://www.waldomaths.com/ Enlarge1NL.jsp
  14. 14. Ray Method Video
  15. 15. Very Useful
  16. 16. Very UsefulStep 1
  17. 17. Very UsefulStep 1
  18. 18. Very UsefulStep 1Step 2
  19. 19. Very UsefulStep 1Step 2
  20. 20. Step 3
  21. 21. Step 3
  22. 22. Step 3 Step 4
  23. 23. Step 3 Step 4
  24. 24. Step 3 Step 4In this example the scale factor is 3 that’s why every length is being multiplied by 3!
  25. 25. Step 5
  26. 26. Step 5
  27. 27. You try!Enlarge thistriangle bya scalefactor of 3using (2, 1)as thecentre ofenlargement. 1 2
  28. 28. The ResultEnlarge thistriangle by Use the lines toa scale find the cornersfactor of 3 of the enlargedusing (2, 1) shapeas thecentre ofenlargement. Draw lines from the centre of enlargement 1 through the vertices (corners) of the shape. 2
  29. 29. AnotherCentre of Enlargement To enlarge the kite by B scale factor x3 from the point shown. A Object C D
  30. 30. Enlargements from a Given PointCentre of Enlargement X3 To enlarge the kite by B scale factor x3 from the point shown. A Object C B/ 1. Draw the ray lines through vertices. D 2. Mark off x3 distances C/ along lines from C of E. A/ Image 3. Draw and label image. Or Count Squares D/
  31. 31. Properties of enlargements • Shape of image is the same only size has changed. • Angle measures remain the same. • Image length = k (object length) OR • k = Image length/Object length • Area of Image = k^2 (area object) OR • k^2 = Area of Image/Area of object
  32. 32. To Find the Centre of the Enlargement
  33. 33. • 1. Choose two points on the image and their corresponding points on the original figure.• 2. From each of these points on the larger figure, draw a line to the corresponding point on the smaller figure.• 3. Produce these lines until they intersect at the point is the centre of the enlargement.
  34. 34. Example Finding the Centre of Enlargement A/ B/ The small rectangle has been enlarged as shown. Find the centre of enlargement. Image D/ C/A B ObjectD C
  35. 35. Solution
  36. 36. Another
  37. 37. Finding the Centre of Enlargement. B The large kite has been enlarged by scaleA C factor x ! as shown. Find the centre of Object enlargement. A/ Draw 2 ray lines through C/ corresponding vertices to B/ Image locate. D D/ Centre of Enlargement Find Centre 3
  38. 38. This one too
  39. 39. Finding the Centre of Enlargement B The small kite has beenA enlarged as shown. Find Object C the centre of Centre of Enlargement enlargement. D/ D Draw 2 ray lines through corresponding vertices to locate. Image C/ A/ B/ Find Centre 2

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