What is Invariant?

Invariant:
-A figure or property that remains unchanged under a transformation of the plane is referred to as invariant.

                                                            What is Isometry?

Isometry:
-isometry is a transformation of the plane that preserves length

                                                         What is a Glide Reflection?

Glide Reflection:
- a glide reflection is a composition of reflection in a line, then a translation along that line

                          Aim: How do we identify transformations?

Transformation:

- A transformation is when you move a geometric figure.

Types of Transformations:

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

-Rotation=Figure is turned around a single point

-Reflection= Figure is flipped over a line of symmetry

-Dilation=An enlargement or reduction in size of an image 
      

Reflecting over the x-axis: (the x-axis as the line of reflection)

When you reflect a point across the x-axis, the x-coordinate remains the same,
but the y-coordinate is transformed into its opposite. 

The reflection of the point (x,y) across the x-axis is the point (x,-y).      P(x,y) → p' (x,-y) or rx-axis(x,y)=(x,-y)

Hint:  If you forget the rules for reflections when graphing, simply fold your graph paper along the line of reflection (in this example the x-axis) to see where your new figure will be located.  Or you can measure how far your points are away from the line of reflection to locate your new image.  Such processes will allow you to see what is happening to the coordinates and help you remember the rule.

                                                    Aim: How do we graph Dilation's?

Dilation:

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

Scale Factor:
-The ratio by which the image stretches or shrinks is known as the scale factor.
-If the scale factor is >1, then the image is enlarged
-If the scale factor is >0 and <1, then the image will shrink

PROBLEM:  Draw the dilation image of rectangle EFGH with the center of  dilation at point E and a scale factor of 1/2. OBSERVE: Point E and its image are the same.  It is important to observe the distance from the center of the dilation, E, to the other points of the figure.  Notice EF = 6 and E'F' = 3. HINT:  Be sure to measure distances for this problem.