Rigid Motion in a Plane Translations Reflections Rotations
- Slides: 50
Rigid Motion in a Plane * Translations * Reflections * Rotations
MC Esher
* Translations (Slide your image over) * preimage * image
* Reflections (Flip your image over) * preimage * image
* Rotations (Turn your image about a fixed point ) * image * preimage
What are the different transformations?
Naming Transformations 1. Name and describe the transformation. Reflection in the line x = -2 2. Name two angles with the same measure. B and F D and H etc.
In the figure, XYZ → ABC by a transformation. Name the transformation and the image of X. X Z C Reflection about the line. Y B A
Transformations are called RIGID if every image is congruent to its preimage. Rigid transformations can also be referred to as an ISOMETRY. Every segment is congruent to its image.
Which of the following are rigid transformations? (Isometry)
Find the value of each variable, given that the transformation is an isometry.
Translations
B C A
E G F
Sketch the image of the triangle after the translation (x, y) (x + 5, y – 3) (-2, 4) (-6, 1) (3, 1) (-4, 0) (-1, -2) (1, -3)
Reflections
Reflecting across the x-axis… changes the sign of the.
Reflect over the x-axis
Reflecting across the y-axis… changes the sign of the.
Reflect over the y-axis
Reflections in a Coordinate Plane Graph the given reflections. a. A(3, 2) in the y-axis A’(-3, 2) b. B(1, -3) in the line y = 1 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.
• http: //www. adrianbruce. com/Symmetry/
Animals that have Line Symmetry Here 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 14 th 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 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.
Japanese culture dislike exact symmetry more than conventional Western culture. 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.
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 known for having a 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?
- Translations and dilations
- Reflections and translations
- Reflection translation rotation dilation
- Translations reflections and rotations
- Translation vs reflection
- How to verify a congruence transformation
- Identify the transformation
- Trig identities from reflections and rotations
- Slide
- Rotations in the coordinate plane
- Rotational symmetry in maths
- Data plane control plane and management plane
- Rigid vs non rigid transformations
- Overflow and non overflow dams
- Irrational exponential function
- Translation on a coordinate plane worksheet
- Reflections in the coordinate plane
- Plane kinetics of rigid bodies
- Iczv
- Is a dilation a rigid motion?
- Rigid body kinetics
- Rolling motion of a rigid object
- Rigid motion definition
- Introduction rigid motion or isometry
- Rigid body transformation in computer graphics
- Rigid motion in geometry
- Compositions of rigid motions
- 9-3 rotations
- 5-1 rotations
- Lesson 3 rotations
- 9-3 rotations
- Lesson 9 sequencing rotations
- Volleyball rotations 1-6
- Write a rule to describe each transformation
- Rules of rotation
- Lesson 3 rotations answer key
- Rotations and angle terminology
- Revolution vs rotation
- Pnwu clinical rotations
- What is improper rotation
- Volleyball 6-2 rotation
- Volleyball 5-1 rotation
- Zones in volleyball court
- Rotations quiz
- Inverse z-transform solved examples
- 포아송비
- Forward equivalence class
- Motion in a plane
- Does vertical velocity change in projectile motion
- General planar motion
- Rectilinear translation