Aim#5 glide reflection & Isometry

How do we use other definitions of transformations?


 Glide Reflection
- the combination of a reflection in a line and a translation along that line
Examples:

Isometry
- a transformation of the plane that preserves length
 -  a direct Isometry preserves orientations or order the letters on the diagram go in the same clockwise or counter clockwise direction on the figure and it's image .
Example :

 Opposite Isometry 
-changes the order such as the direction
Examples :

Aim#4 Reflections

How Do we Graph Transformations that are Reflections ?

-A reflection; is a transformation that creates figures that are mirrored images of the original.

Examples of Reflections ;

      

- typically , if you are not given or asked to graph a reflection directly , you can still show reflection through your coordinates;

 - To reflect in the x-axis (x,y) -> ( x,-y)

 - To reflect in the y-axis (x,y) -> ( -x,y)

For example: What are the coordinates of the points ( 4,6) reflected in the y- axis ?

                       y- axis ( x,y) -> (-x,y)  Answer : ( -4,6)

Aim#3 Dilations

 How Do We Graph Dilations ?


Definition of a Dilation
- A dilation is a type of transformation that causes an image to stretch or shrink in porportion to its original or regular size.
Examples:

Scale Factor
- the scale factor is the ratio by which the images stretch or shrink
- If the scale factor is greater than one ( >1), then the image is enlarged
-If 0 & 1 is greater than ( <0 & <1) the scale factor, then the image will shrink
- Multiple the dimensions of the original image by the scale factor  to get the dimensions of the dialated image.
 The following remain the same :
-Angle measures
- points on a line
- midpoint of an image
- orientation of the image
- irregular polygons if the sides follow the same scale factor

When expressing Dilations :
- when you are asked or expressed dilation you will see it written as for examples D2 or D-2

aim#2 :Rotations

How Do We Graph Rotations?

Definition of a Rotation
- A rotation is when a geometric figure is turned around a single point
Examples:

Describing a Rotation
1) Angle of rotation
2) A direction ( clockwise or counter clockwise, do as directed)
3) A center of rotation

- When graphing rotations you can also switch the coordinates accordingly, depending on the degree of the rotation :
 90 degrees = ( x,y) -> (-y,-x)
180 degrees = (x,y) -> (-x,-y )
270 degrees = ( x,y) -> (y,-x)

An example problem is: What is the image of the coordinates (-4,-5) under the transformation ry-axis?
                                             Answer : (4,-5)

How to Identify Transformations

 How do we Identify transformations?


- You can identify a transformation by recognizing that a transformation, by definition is to move a geometric figure.


 Types of transformation
Translation- every point is moved the same distance in the same direction
Ex:
Reflection- when a figure flipped over a line of symmetry
Ex:
Rotation- When a figure is turned around a single point
Ex:
Dilation- an enlargement or reduction insize or image
Ex: