How do we solve compositions of transformation problems ?

composition of transformation - when you have two or more transformations that are combined to form  a new transformation , the result is called a composition of transformation

when solving a composition you will do the second part first then the first part .

How do we use the other definitions of Transformations ?

Glide relfection - the combination of a reflection in a line and a translations along that line .

Orientation - orientation refers to the arrangement of points , relative to one another , after a tranformation  has occurred .

Isommetry - an isommetry is a transformation of the plane that preserves length

Direct isommetry - orientation of the isommetry remains the same .

Opposite isommetry - an isommetry that changes the order such as something going  from clockwise to counter clockwise .

Invareant - a  figure or property that remains unchanged under a transformation of the plane is referred to as invareant . ( no varreation have occurred )

How do we Graph Dilation's ?

Dilation- is a type of translation that causes an image to stretch or shrink in proportion to its original size .

scale size - the rotation by which the image stretches or shrinks is known as the scale factor . If the scale factor is  grater then 1 then  it will be enlarged . if the image scale factor is >0 and <0 then the image will shrink .

NOW YOU ARE READY TO GRAPH DILATION'S !

How do we Graph Rotations ?

Describing Rotations -
1) Angle of rotation
2) a direction (clockwise or counterclockwise )
3) center of rotation
       
when solving for a rotation you may also be able to use a formula ; i prefer the formula :

90 degrees -
(A,B)------->(-B,A)

180 degrees -
(A,B)-------->(-A,-B)

270 degrees -
(A,B)-------->(B,-A)

note :
   Whenever the problem does not state it is clockwise it is automatically counter clockwise , but the the formula will switch the problem for you automatically .

How do we Graph Transformations that are Reflections ?

Reflections - Line of symmetry
       * A figure has a line of symmetry  , if a line can be drawn down the figure so that it divides the figure into a mirror image

Line of reflection -
    (FLIP) a transformation that creates figures which are mirror images .

           x-axis    (x,y)-------------(x,-y)
          y-axis     (x,y)-------------(-x,y)

How do we Identify Transformations

Objective - Identify transformations including transformations such as Rotation , Reflection , and Dialation , and Transformation .

Transformation - When you move a figure .

Translation - Every point is moved the same distance in the same direction

Reflection - A figure flipped over a line of symmetry

Rotation -Figure is turned around a single point .

Dialation - Enlargement or reproduction in size of an image .