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Notes Dilations

Notes Dilations. Definitions. Dilation - a transformation in which every point P has an image P' placed on OP so that and OP' = k * OP Center of Dilation – the point from which an original figure is dilated.

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Notes Dilations

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  1. Notes Dilations

  2. Definitions Dilation - a transformation in which every point P has an image P' placed on OP so that and OP' = k * OP Center of Dilation – the point from which an original figure is dilated. Scale Factor - the ratio of the image length to the corresponding original length.

  3. Scale Factor • If the scaled factor is greater than 1, then it is an enlargement (k>1). • If the scaled factor is equal to 1, then it is a congruent figure (k=1) • If the scale factor is less than 1, then it is a reduction (k<1).

  4. 4 2 = k = = 2 Scale Factor Image Distance Corresponding distances Original Distance 2 > 1 This dilation is an enlargement .

  5. 2 3 = k = Scale Factor Image Distance Corresponding distances Original Distance 2/3 < 1 This dilation is an reduction.

  6. Example: • Rectangle W’X’Y’Z’ is the image of rectangle WXYZ after a dilation. • Find the scale factor of the dilation. • Tell whether the image is a reduction or an enlargement.

  7. Example: 2.

  8. Example: 3.

  9. Reduction, Enlargement, or Congruent? • K = 4 • K = ½ • K = 1 4>1 Enlargement ½ <1 Reduction Congruent

  10. Matching • K = ¼ • K = 3 • K = 2/7 • K = 1 • K = 5 • K = 3/8 Reduction Enlargement Congruent

  11. 7. scale factor 2

  12. 8. scale factor ¼

  13. 8. scale factor 1/3

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