Transformations
transformation
•A change of position
or size of a figure.
1.Translations
4 types:
2.Reflections
3.Rotations
4.Dilation
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.
Example
Does Rhombus MATH have
point symmetry? Yes
A
M
T
H
rotation
• A transformation that
turns a figure about a
fixed point.
Fixed point
Example:
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 Yes
• Reflection Yes
• Rotation Yes
• Dilation No
Transformations
are used to make
tessellations
tessellation
• A repeating pattern of
figures that completely
covers a plane without
gaps or overlaps.
Transformations
in the work of
M.C. Escher
Learn more about
M.C. Escher
• http://www.mcescher.com/