Geometry Unit 4

rigid motion (isometry)

a transformation that preserves size and shape

What are the 4 types of transformations?

translation, rotation, reflection, dilation

translation

moves every point of a figure the same distance and same direction, slides

rotation

turns a figure about a fixed point called the center of rotation, turns 

reflection

uses a line of reflection to create a mirror image of the original figure, flip

dilation

enlarges or reduces a figure in regards to a fixed point, smaller bigger

what is translation notation

T(x,y) —> (x+ b, y+a)

vector

a quantity that has both direction magnetude or size has an initial point or start and a terminal point or end

component form

< change us x, change in y >

composition of translations

two or more combined translations

if x,y is reflected over the x-axis then its image is the point:

x,-y

if x,y is reflected over the y-axis then its image is the point:

-x,y

if x,y is reflected over the y=x then its image is the point:

y,x

if x,y is reflected over the y=-x then its image is the point:

-y,-x

2 reflections back-to-back over parellel lines are the same as a … 

translation

Glide reflection

a transformation that involves a translation and a reflection

line of symmetry

a line that divided a figure into two parts such that each part in a mirror image of the other

what is rotation notation?

R(point of rotation, degrees)

Unless otherwise stated rotations will always be…

counterclockwise

for a rotation of 90 x,y—>

-y,x

for a rotation of 180 x,y—>

-x-y

for a rotation of 270 x,y—>

y,-x

for a rotation of 360 x,y—>

x,y

What is the order of a figure?

the amount of rotation that can be performed mapping the figure onto itself

a plane has rotational symmetry if…

it can be mapped onto itself by a rotation of 180% or less

what is the angle of rotational symmetry?

is 360/ the order