Students ppp 2

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Students ppp 2

  1. 1. Transformations<br />Reflections<br />
  2. 2. Transformation<br />A transformation is a change in position, shape, or size of a figure<br />
  3. 3. Reflections<br />
  4. 4. Reflections<br />Did you take a look in the mirror this morning? You were actually the Pre-image, or the original figure. The view you caught in the mirror was your image, or the figure after a transformation<br />
  5. 5. Reflections<br />Leonardo da Vinci’s writings were the pre-image. <br />In order to read them, you must hold them up to a mirror, then read the image<br /> <br />
  6. 6. A reflection can be seen in water or in a mirror. An object and its reflection have the same shape and size, but the opposite orientation. <br />
  7. 7. Reflections<br />? ? ? ? ? ? ? ? ? ? ? ? ?<br />What are some types of reflections?<br />
  8. 8. Reflections<br />There are reflections along the vertical lines<br />
  9. 9. Reflections<br />Reflections along a horizontal <br />Line,<br />
  10. 10. Reflections<br />And reflections along a diagonal<br />Line!<br />
  11. 11. Reflections<br />A transformation maps the pre-image onto its image. Take a look at the example below:<br />The above statement would be read “Triangle FUN maps to triangle Fprime, Uprime, Nprime”. Notice that prime notation is used to identify points on the image.<br />
  12. 12. Reflections<br />
  13. 13. Reflections<br />
  14. 14. Reflections<br />
  15. 15. Reflection<br />A reflection reverses the orientation of a figure. The image will always appear reversed from the pre-image<br />
  16. 16. Reflections<br />Based on what we have learned so far, can anyone predict what the two main properties of reflections are?<br />
  17. 17. Reflection<br />Just to make sure it is crystal clear……….<br />Is the figure on the right side of the mirror line a reflection of the figure on the left side of the mirror line?<br />
  18. 18. Reflection<br />Is the figure on the right side of the mirror line a reflection of the figure on the left side of the mirror line?<br />
  19. 19. Reflections<br />Let’s relate our knowledge of reflections to what we know about the coordinate system.<br />Suppose we have coordinate points A(3,1), B(4,2), and C(3,5). If we reflected these points over the x-axis, what would be the coordinates of their images, A’, B’, and C’? Can you find a pattern and make a generalization for the mapping of any point (x, y) to its image?<br />
  20. 20. Reflections<br />Let’s try another one. Use the same points as above with A(3,1), B(4,2), and C(3,5). If we reflected these points over the y-axis, what would be the coordinates of their images, A’, B’, and C’? Can you find a pattern and make a generalization for the mapping of any point <br />(x, y) to its image?<br />
  21. 21. Reflections<br />General rule of finding the image of a point over a mirror line:<br />Draw a perpendicular line from the pre-image point to the mirror line and extend the line the same distant to reach the image point<br />A pre-image<br />image A’<br />Mirror line<br />
  22. 22. Something to think about…..<br />According to the wall street journal, most drugs are made up of two versions of the same molecule. One version is called an R-isomer, the other version is called an S-isomer, and they are mirror images of each other with different healing properties. In an effort to produce drugs with fewer side effects, researchers have learned to produce pure batches of these isomers. They run tests to see which version has the least amount of side effects, then produce the drug from this batch. For example, R-isomer of Alboterol treats asthma, but its mirror image (the S-isomer) has shown to increase the risk of future heart attacks.<br />Pretty neat, huh? GEOMETRY IS EVERYWHERE!<br />

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