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Enlargement

Learn how to enlarge 2D shapes using scale factors and locate the centre of enlargement. Practice exercises included.

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Enlargement

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  1. Enlargement Objectives: F Grade Give a scale factor of an enlarged shape E Grade Enlarge a shape by a positive scale factor Find the measurements of the dimensions of an enlarged shape D Grade Enlarge a shape by a positive scale factor from a given centre C Grade Find the centre of enlargement

  2. Enlargement A 2-D shape can be made larger by a given amount This is called the Scale Factor object w image 2w l 2l Notice how the sides of the image are twice that of the object This is an enlargement scale factor 2 If the length the sides was increased to be 3 times as long the scale factor would be 3

  3. Enlargement Objects can be enlarged using the scale factor to extend the length of the sides, because it is the sides that are increased it is called the linear scale factor. As was seen by finding the length of the image side by: image line length = object line length × scale factor similarly linear scale factor = object line length image line length This name is only important when the area and / or volume are part of the consideration for enlargement.

  4. Now do these: Enlargement Enlarge these shapes alongside by a scale factor of 2 1. 3. 2. Enlarge these shapes below by a scale factor of 3 5. 4.

  5. Enlargement Identify the scale factor used to enlarge these shapes 6. 8. 7. scale factor 2.5 scale factor 3 scale factor 4

  6. Enlargement Normally an enlargement is required given a centre of enlargement. Using the centre of enlargement locates the image. Draw construction lines from the centre of enlargement CoE through the vertices of the object. Ray Lines Using a scale factor 2 the distance from the CoE to the image vertices is 2 times the distance from the CoE to the object vertices. CoE object 5 squares right 1 square down Scale Factor 2 Distance from CoE 10 squares right 2 squares down 2 squares right 1 square down x x Scale Factor 2 Distance from CoE 4 squares right 2 squares down 2 squares right 3 squares down Scale Factor 2 Distance from CoE 4 squares right 6 squares down x This gives us enough information to draw the image

  7. Enlargement Repeat this to see the effect of a scale factor 3 5 squares right 1 square down CoE object Scale Factor 3 Distance from CoE 15 squares right 3 squares down 2 squares right 1 square down x x Scale Factor 3 Distance from CoE 6 squares right 3 squares down 2 squares right 3 squares down x Scale Factor 3 Distance from CoE 6 squares right 9 squares down This gives us enough information to draw the image

  8. Enlargement The position of the centre of enlargement relative to the object makes a difference as to where the enlarged image is positioned. CoE CoE CoE CoE CoE CoE CoE CoE CoE Moving the centre of enlargement away from the object moves the image further away in the opposite direction Moving the centre of enlargement up moves the image down Moving the centre of enlargement down moves the image up

  9. Enlargement Find the coordinates of the centre of enlargement by drawing the ray lines 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 0 8 8 1 1 2 2 3 3 4 4 5 5 6 6 7 7 10 10 -10 -10 9 9 -8 -8 -9 -9 -3 -3 -6 -6 -4 -4 -7 -7 -5 -5 -2 -2 -1 -1 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 -6 -6 -7 -7 -8 -8 -9 -9 -10 -10

  10. Identify the scale factor used to enlarge these shapes 6. 8. 7. 3. Enlargement 5. Enlarge these shapes alongside by a scale factor of 2 Enlarge these shapes below by a scale factor of 3 2. Worksheet 1 1. 4.

  11. Worksheet 2 Enlargement Enlarge these shapes using the ray line method and C as the centre of enlargement Find the coordinates of the centre of enlargement by drawing the ray lines scale factor 2 1. scale factor 3 2. C x 10 C x 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 0 8 8 10 10 1 1 2 2 3 3 4 4 5 5 6 6 7 7 9 9 -10 -10 -3 -3 -9 -9 -8 -8 -2 -2 -4 -4 -7 -7 -6 -6 -5 -5 -1 -1 3. -1 -1 -2 -2 -3 -3 -4 -4 4. -5 -5 scale factor 2.5 -6 -6 -7 -7 -8 -8 -9 -9 -10 -10 C x C x scale factor 3

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