Symmetries Flashcards
One - to - one transformation
if no two points are moved into a single position
onto transformation
if all the positions in the plane are achieved by some points in the rearrangement
bijection
a transformation that is both one - to - one and onto
transformation
a rearrangement of all the points in the plane
Rigid transformations
a transformation that preserves distances, aka symmetries
What are symmetries always?
bijections
What are the ____ types of symmetries
Rotations, Translations, Reflections `
A point is moved around O at 45 degrees, what is this symmetry
a rotation
How do you know if a rotation is a symmetry
it is a rigid transformation; if point A and B is moved around point O, for each point A and B the distance is the same as image points f(A) and f(B), it is preserving the distance between the two points
Every point in a plane is moved along a fixed vector, what is this symmetry
a translation
What is a vector
another word for oriented arrow
Points moved across a specific line, what is this symmetry and what is the name of this line?
a reflection, and the line of reflection
What direction do possitive angles rotate in?
counterclockwise
What direction do negative angles rotate in
clockwise
What is important to remember when it comes to negative rotations
the rotation of -60 dgrs moves the point in a plane the same way as +300 dgrs, we still consider these translations equal
