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Transformation Geometry Dilations

Transformation Geometry Dilations. What is a Dilation?. Dilation is a transformation that produces a figure similar to the original by proportionally shrinking or stretching the figure. Dilated PowerPoint Slide. Proportionally. Let’s take a look….

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Transformation Geometry Dilations

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  1. Transformation Geometry Dilations

  2. What is a Dilation? • Dilation is a transformation that produces a figure similar to the original by proportionally shrinking or stretching the figure. Dilated PowerPoint Slide

  3. Proportionally Let’s take a look… And, of course, increasing the circle increases the diameter. • When a figure is dilated, it must be proportionally larger or smaller than the original. So, we always have a circle with a certain diameter. We are just changing the size or scale. Decreasing the size of the circle decreases the diameter. We have a circle with a certain diameter. • Same shape, Different scale.

  4. A HINT: SAME SHAPE, DIFFERENT SIZE C D B Which of these are dilations??

  5. Scale Factor and Center of Dilation When we describe dilations we use the terms scale factor and center of dilation. • Scale factor • Center of Dilation Here we have Igor. He is 3 feet tall and the greatest width across his body is 2 feet. He wishes he were 6 feet tall with a width of 4 feet. His center of dilation would be where the length and greatest width of his body intersect. He wishes he were larger by a scale factor of 2.

  6. Scale Factor • If the scale factor is larger than 1, the figure is enlarged. • If the scale factor is between 1 and 0, the figure is reduced in size. Scale factor > 1 0 < Scale Factor < 1

  7. Are the following enlarged or reduced?? C A Scale factor of 1.5 D Scale factor of 3 B Scale factor of 0.75 Scale factor of 1/5

  8. B’ C’ A’ B A C The Object and the Image • The original figure is called the object and the new figure is called the image. • The object is labeled with letters. • The image may be labeled with the same letters followed by the prime symbol. Image Object

  9. Dilations Used Everyday

  10. Remember • Dilations areenlargementsorreductions.

  11. How do we use scale factor? • We can multiply the scale factor by each coordinate: Scale factor = 1/3 A (3, 9) , B (15, -6), C (6, 0) 1/3 * A(3, 9)  A’ (1, 3) 1/3 * B(15, -6)  B’ (5, -2) 1/3 * C(6, 0)  C’ (2, 0)

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