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Dilations - PowerPoint PPT Presentation

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Dilations
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  1. Dilations

  2. 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

  3. A dilation is ALWAYS similar to the original figure. So the corresponding angles are congruent and corresponding sides are proportional. • Scale Factor: The ratio of a length on the image to a length on the original figure is the scale factor of the dilation.

  4. Examples 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.

  5. Find the coordinates of the image of triangle JKL after a dilation with each scale factor. Then graph JKL and J’K’L’. • A) Scale Factor 3 • B) Scale Factor 1/3

  6. Find and Classify a Scale Factor • 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)

  7. Write a ratio of the x-or the y-coordinate of one vertex of the DILATION to the x- or y-coordinate of the CORRESPONDING vertex of the original figure. • Let’s use V and V’ since we have whole numbers. • V (-2, 2) • V’ (-5, 5) Y-coordinate of V’ = 5 Y-coordinate of V 2

  8. Our scale factor is 5/2 • 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

  9. 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