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Dilations Learning: Transforming Figures using Dilations

Learn about dilations, a transformation that produces similar figures by proportionally shrinking or stretching them. Explore examples and understand the concept of scale factor.

katherinebryant
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Dilations Learning: Transforming Figures using Dilations

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  1. DilationsLearning Target: I can transform figures using 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. • A dilation is a transformation who preimage and image are similar. A dilation isnot an isometry. 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 • 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

  6. 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

  7. Dilations Used Everyday

  8. Links • http://www.mathopenref.com/dilate.html

  9. Examples Caution: Make sure you read the ratio sentence carefully. Image is to Pre - Image • Write the sentence as a ratio to get Scale Factor (S/F): • For this sentence: • Dashed / Solid • 8 / 4 = 2 greater than 1 is an enlargement • 9 / 3 = 3 greater than 1 is an enlargement • 6 / 9 = 2/3 less than 1 is a reduction • 8 / 4 = 2 greater than 1 is an enlargement.

  10. Examples Multiply each part of the coordinate by the scale factor: • (2, 3) ; 6 multiply both x and y by 6 B’(12, 18) • 6. (0, -5) ; 2/5 multiply both x and y by 2/5 A’(0, -2)

  11. Examples P ( 0, 4) P’ (0, 2) E (6,6) E’ (3,3) N (4, 0) N’(2,0) T (0, -4) T’ (0, -2) A(-2, 0) A’ (-1, 0) Check/Compare your graph with person next to you.

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