transformations
DESCRIPTION
Transformations. transformation. A change of position or size of a figure. Translations Reflections Rotations Dilation. 4 types:. translation. A transformation that moves points the same distance and in the same direction. * The figures are congruent!. * The original image is slid!. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/1.jpg)
TransformationsTransformationsTransformationsTransformations
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transformation•A change of position or size of a figure.
1.Translations
2.Reflections
3.Rotations
4.Dilation
4 types:
![Page 3: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/3.jpg)
translation• A transformation that moves points the same distance and in the same direction.* The figures are congruent!
* The original image is slid!
![Page 4: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/4.jpg)
Example:
![Page 5: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/5.jpg)
reflections• The mirror image of the original figure
* The figures are congruent!
* The original image is flipped!
![Page 6: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/6.jpg)
Example:
Line of Reflection
![Page 7: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/7.jpg)
The line of Reflection is also called the line of
symmetry.
![Page 8: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/8.jpg)
It is also possible to have a
reflection image with respect to a
point.
![Page 9: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/9.jpg)
Point of Symmetry• The point must be the midpoint for all segments that pass through it and have endpoints on the figure.
![Page 10: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/10.jpg)
ExampleDoes Rhombus MATH have point symmetry?
M
A T
H
Yes
![Page 11: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/11.jpg)
rotation• A transformation that turns a figure about a fixed point.
Example:
Fixed point
![Page 12: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/12.jpg)
Another Example:
![Page 13: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/13.jpg)
Dilation• Change in size of a figure
–Enlarge or shrink
–Similar figures (congruent angles, proportional side lengths)
![Page 14: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/14.jpg)
Original Figure
![Page 15: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/15.jpg)
isometry• Congruence Transformation
–Maps every segment to a congruent segment
• No change in size!
–Congruent sides and congruent angles
![Page 16: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/16.jpg)
State whether each of the following have isometry.• Translation
• Reflection
• Rotation
• Dilation
YesYe
s
No
Yes
![Page 17: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/17.jpg)
Transformationsare used to make
tessellations
![Page 18: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/18.jpg)
tessellation• A repeating pattern of figures that completely covers a plane without gaps or overlaps.
![Page 19: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/19.jpg)
TransformationsTransformationsin the work ofin the work ofM.C. EscherM.C. Escher
TransformationsTransformationsin the work ofin the work ofM.C. EscherM.C. Escher
![Page 20: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/20.jpg)
![Page 21: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/21.jpg)
![Page 22: Transformations](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5681458c550346895db274cf/html5/thumbnails/22.jpg)
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