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* Translations
* Reflections
* Rotations
Rigid Motion in a Plane
MC Esher
* Translations
* preimage * image
(Slide your image over)
* Reflections
(Flip your image over)
* preimage * image
* Rotations(Turn your image about
a fixed point )
* preimage
* image
What are the different transformations?
Naming Transformations
1. Name and describe the transformation.
2. Name two angles with the same measure.
Reflection over the line x = -2
B and F
D and H
etc.
In the figure, XYZ → ABC by a transformation. Name the transformation and the image of X.
AX
YZ
A
BC
Reflection over the given line.
Rigid transformations can also be referred to as an ISOMETRY.
Every segment is congruent to its image.
Transformations are called RIGID if every image is congruent to its preimage.
Which of the following are rigid transformations?
(Isometry)
Find the value of each variable, given that the transformation is an isometry.
72 x6
23 y10
4 ,12 yx
Translations
A
B
C
F
E
G
Sketch the image of the triangle after the translation (x, y)(x + 5, y – 3)
(-6,1)
(-4,0)
(-2,4)
(-1,-2)(1,-3)
(3,1)
Reflections
Reflecting across the x-axis… changes the sign of the .
( , ) ( , )x y x y
( , ) ( , )x y x y ( , ) (3 1 , )
( , ) ( 2 3 , )( , ) ( 3 3 , )( , ) (1 4 , )
Reflect over the x-axis
Reflecting across the y-axis… changes the sign of the .
( , ) ( , )x y x y
( , ) ( , )x y x y ( , ) (2 4 , )
( , ) ( 1 8 , )( , ) ( 4 4 , )( , ) (2 5 , )
Reflect over the y-axis
Reflections in a Coordinate Plane
Graph the given reflections.
a. A(3, 2) in the y-axis
b. B(1, -3) in the line y = 1
A’(-3, 2)
B’(1, 5)
Line of symmetry – a line that can be drawn through a figure so that the part of the figure on one side of the line is the congruent reflected image of the part on the other side of the line.
Animals that have Line Symmetry Here are a few more great examples of mirror image in
the animal kingdom.
The Taj Mahal Symmetry exists in architecture all around the world.
One of the best known examples of this is the Taj Mahal.
It was completed in 1630 by the Indian ruler Shahs Jahan as a tomb for his favorite wife Mumtaz Mahal who
died as a result of giving birth to their 14th child. To build this tomb it took 20,000 workers, 20 years (Encarta 97) and it is rumoured that they used 40,000 elephants
to transport the materials.
Symmetry of Drains
Drains can have many different orders of rotational symmetry, Have a look at some of the drains in your home or at school and see what order of rotation or line symmetry they have.
These masks have a line of symmetry from the forehead to the chin.
Ex. Determine the number of lines of symmetry in the quadrilateral
Ex. 1: Find all lines of symmetry.
Symmetry is found everywhere in nature and is also one of the most prevalent themes in art, architecture, and design. Symmetry is certainly one of the
most powerful and pervasive concepts in mathematics.
Symmetry appears as being too perfect for their liking. It is too
unnatural and sterile.
The Japanese hold the view that their lives always need refinement and room for growth, complete
symmetry implies perfection and so is undesirable.
Japanese culture dislike exact symmetry more than conventional Western culture.
If something has a pattern it is easier to spot the out of place and therefore possibly dangerous.
Most plants and animals are symmetrical
Symmetrical flowers are more attractive to bees because they have more
nectar.
Symmetric objects are usually more pleasing to look at than asymmetric ones.
Symmetry is an indication
of both youthfulness and health.
Denzel Washington is said to have a
very symmetrical
face.
Greta Garbo was Greta Garbo was known for having a known for having a
very symmetrical face.very symmetrical face.
“Christy Turlington has attributed much of
her success as an advertising icon to the perfect symmetry of
her lips.”
Asymmetry
Facial asymmetry
is an indication of
aging.
Is the Face Really Symmetrical?
http://www.adrianbruce.com/Symmetry/
Is the Face Really Symmetrical?
Is the Face Really Symmetrical?
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