Date post: | 22-May-2015 |
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Education |
Upload: | msedaghatian1 |
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2. Transformation
A transformation is a change in position, shape, or size of a
figure
3. Reflections
4. Reflections
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
5. Reflections
Leonardo da Vincis writings were the pre-image.
In order to read them, you must hold them up to a mirror, then read
the image
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.
7. Reflections
? ? ? ? ? ? ? ? ? ? ? ? ?
What are some types of reflections?
8. Reflections
There are reflections along the vertical lines
9. Reflections
Reflections along a horizontal
Line,
10. Reflections
And reflections along a diagonal
Line!
11. Reflections
A transformation maps the pre-image onto its image. Take a look at
the example below:
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.
12. Reflections
13. Reflections
14. Reflections
15. Reflection
A reflection reverses the orientation of a figure. The image will
always appear reversed from the pre-image
16. Reflections
Based on what we have learned so far, can anyone predict what the
two main properties of reflections are?
17. Reflection
Just to make sure it is crystal clear.
Is the figure on the right side of the mirror line a reflection of
the figure on the left side of the mirror line?
18. Reflection
Is the figure on the right side of the mirror line a reflection of
the figure on the left side of the mirror line?
19. Reflections
Lets relate our knowledge of reflections to what we know about the
coordinate system.
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?
20. Reflections
Lets 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
(x, y) to its image?
21. Reflections
General rule of finding the image of a point over a mirror
line:
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
Apre-image
imageA
Mirror line
22. Something to think about..
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.
Pretty neat, huh? GEOMETRY IS EVERYWHERE!