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TransformationsTransformationsTransformationsTransformations
transformation•A change of position or size of a figure.
1.Translations
2.Reflections
3.Rotations
4.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!
Example:
reflections• The mirror image of the original figure
* The figures are congruent!
* The original image is flipped!
Example:
Line of Reflection
The line of Reflection is also called the line of
symmetry.
It is also possible to have a
reflection image with respect to a
point.
Point of Symmetry• The point must be the midpoint for all segments that pass through it and have endpoints on the figure.
ExampleDoes Rhombus MATH have point symmetry?
M
A T
H
Yes
rotation• A transformation that turns a figure about a fixed point.
Example:
Fixed point
Another Example:
Dilation• Change in size of a figure
–Enlarge or shrink
–Similar figures (congruent angles, proportional side lengths)
Original Figure
isometry• Congruence Transformation
–Maps every segment to a congruent segment
• No change in size!
–Congruent sides and congruent angles
State whether each of the following have isometry.• Translation
• Reflection
• Rotation
• Dilation
YesYe
s
No
Yes
Transformationsare used to make
tessellations
tessellation• A repeating pattern of figures that completely covers a plane without gaps or overlaps.
TransformationsTransformationsin the work ofin the work ofM.C. EscherM.C. Escher
TransformationsTransformationsin the work ofin the work ofM.C. EscherM.C. Escher
