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Dilations. Vocabulary. Dilation: The image created by enlarging or reducing a figure. Center: The center of a dilation is a fixed point used for measurement when altering the size of the figure.

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Presentation Transcript

Vocabulary
Vocabulary

  • Dilation: The image created by enlarging or reducing a figure.

  • Center: The center of a dilation is a fixed point used for measurement when altering the size of the figure.

  • Enlargement: An image that is larger than the original figure. An enlargement has a scale factor greater than 1.

  • Reduction: An image that is smaller than the original figure. A reduction has a scale factor between 0 and 1



Examples
Examples corresponding angles are congruent and corresponding sides are proportional.

Graph JKL with vertices

J (3,8), K (10,6), and L (8,2). Then graph its image J’K’L’ after a dilation with a scale factor of ½.



Find and classify a scale factor
Find and Classify a Scale Factor dilation with each scale factor. Then graph JKL and J’K’L’.

  • Quadrilateral V’Z’X’W’ is a dilation of quadrilateral VZXW. Find the scale factor of the dilation, and classify it as an enlargement or a reduction.

    Graph V’Z’X’W’ Graph VZXW

    V’ (-5, 5) V (-2,2)

    Z’ (-2.5, 7.5) Z (-1, 3)

    X’ (2.5, 6) X (1, 2.5)

    W’ (5, 2.5) W (2, 1)



  • Our scale factor is 5/2 the DILATION to the x- or y-coordinate of the CORRESPONDING vertex of the original figure.

  • Based on our scale factor our image is an enlargement since 5/2 is greater than 1.

  • Remember 5/2 is an improper fraction so if we change this into a mixed number we get 2.5


Carleta’s optometrist dilates her pupils by a factor of 5/3. if her pupil before dilation has a diameter of 5 milimeters, find the new diameter after her pupil is dilated


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