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Lesson 84

Lesson 84. Dilations. Vocabulary Review. Transformation – a change in position, size, or shape of a figure Preimage – the original figure in the transformation Image – the shape that is the result of the transformation

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Lesson 84

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  1. Lesson 84 Dilations

  2. Vocabulary Review Transformation – a change in position, size, or shape of a figure Preimage – the original figure in the transformation Image – the shape that is the result of the transformation Isometry – a transformation that does not change the size or shape of the figure

  3. Dilations Vocabulary Dilation is a transformation that changes the size of a figure but not its shape Not Isometry Image and Preimage are similar, but not congruent

  4. Dilations Vocabulary continued Reduction or Contraction – a dilation that results in a smaller figure Enlargement or Expansion – a dilation that results in a larger figure Scale factor – the multiplier used in a dilation Center of dilation – the intersection of lines that connect each corresponding point of the image and preimage The dilation to the right is a reduction, scale factor ½ and center is point E

  5. Dilation of a segment Apply a dilation to using C as a center and a scale factor of 3.

  6. Dilation of a segment Apply a dilation to using C as a center and a scale factor of 3.

  7. Dilation of a segment Apply a dilation to using C as a center and a scale factor of ½.

  8. Dilation of a segment Apply a dilation to using C as a center and a scale factor of ½.

  9. Dilation of a triangle Graph the triangle and its image after a dilation centered at the origin and a scale factor of ½ Write the transformation mapping

  10. Dilation of a triangle Graph the triangle and its image after a dilation centered at the origin and a scale factor of ½ Write the transformation mapping

  11. Applying dilation to real life examples Suppose you want to enlarge a map that is 12 inches by 18 inches. If you choose the 120% enlargement setting on the scanner: • What will be the new lengths of the sides? • How will the perimeter of the original compare to the new? • How will the area of the original compare to the new?

  12. Applying dilation to real life examples Suppose you want to enlarge a map that is 12 inches by 18 inches. If you choose the 120% enlargement setting on the scanner: • What will be the new lengths of the sides? 120% = 1.2 scale factor 12(1.2) = 14.4 in 18(1.2) = 21.6 in

  13. Applying dilation to real life examples Suppose you want to enlarge a map that is 12 inches by 18 inches. If you choose the 120% enlargement setting on the scanner: • How will the perimeter of the original compare to the new? 120% = ? What do you think? This is a comparison of the new to the original. To answer the question we need the reciprocal. The original perimeter is of the new perimeter.

  14. Applying dilation to real life examples Suppose you want to enlarge a map that is 12 inches by 18 inches. If you choose the 120% enlargement setting on the scanner: • How will the area of the original compare to the new? is the ratio of the perimeters Any suggestions? Do we really have to find the areas?

  15. Review / Questions When a dilation is applied, it also affects the distance the image is from the center Percent's are ratios Concentric circles can be looked at as a dilation

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