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Enlargements - Ray Method
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Enlargements - Ray Method

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Enlargements - Ray Method Enlargements - Ray Method Presentation Transcript

  • Enlargements2.4 Transformation Geometry
  • 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.
  • Picture
  • 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
  • • 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.
  • Slide ProjectorDesign
  • Better?• In this case, the light bulb is the centre of enlargement!• C. of E. is the point from which the E. is constructed.
  • Toy Model
  • Toy Model
  • Toy Model
  • 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
  • In Action http://www.ngfl-cymru.org.uk/vtc/ngfl/maths/echalk/enlargement/intro/enlargementIntro.html
  • • 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
  • Ray Method Video
  • Very Useful
  • Very UsefulStep 1
  • Very UsefulStep 1
  • Very UsefulStep 1Step 2
  • Very UsefulStep 1Step 2
  • Step 3
  • Step 3
  • Step 3 Step 4
  • Step 3 Step 4
  • Step 3 Step 4In this example the scale factor is 3 that’s why every length is being multiplied by 3!
  • Step 5
  • Step 5
  • You try!Enlarge thistriangle bya scalefactor of 3using (2, 1)as thecentre ofenlargement. 1 2
  • 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
  • AnotherCentre of Enlargement To enlarge the kite by B scale factor x3 from the point shown. A Object C D
  • 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/
  • 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
  • To Find the Centre of the Enlargement
  • • 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.
  • 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
  • Solution
  • Another
  • 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
  • This one too
  • 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