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What is a Dilation?

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. Transformation Geometry Dilations. Proportionally. Let’s take a look….

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What is a Dilation?

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  1. 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

  2. Transformation Geometry Dilations

  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. Using the scale factor to dilate • A triangle has vertices A(4, -4), B(8,2) and C(8, -4). The image of triangle ABC after a dilation with a scale factor of ½ is triangle DEF. Find the coordinates and sketch the graph.

  8. 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

  9. Book Practice pg 412 #5, 10, 12 • Use graph paper if applicable.

  10. 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

  11. Dilations Used Everyday

  12. Remember • Dilations areenlargementsorreductions. • What are some things that you would not mind dilating to make larger or smaller? Practice Dilation Quiz

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