Aim: How do we use the other definitions of transformations?

There are 4 main types of transformations, but there are many more. The main four are:

• Rotation:  The distance from the center to any point on the shape stays the same.

This ballerina is rotating
360 degrees consistantly.
She is rotating from her heel
on her left foot.

• Translation:  When an image moves by changing it's coordinates by equal distance, same direction, and that the figure stays the same size.

A students drawing of  their
ΔABC being translated by T(7,4).

• Reflection: when an image is reflected over a line to create a mirror image. 

The woman in this picture is
being reflected by the
lake in front of her.

• Dilation: when an image is enlarged or shrunk from its original being. 

The image that Homer is
holding, is the image that
the screen keeps
dilating into.

                           

This person's pupil is
dilated due to being horrified.

                                   
There are many more transformations out there ! But try this little problem:

Aim: What is Isometry?

• The definition of Isometry:

                                - Basically the distance from an original figure (& it's points) and their transformed figure (& their points). 

An example of how ΔABC's points are equally distanced
from  ΔA'B'C' points. This is shown by translation. 

• From the types of Transformations only Reflection, Rotation, and Translation are isometries. Dilation on the other hand, is not a isometry.

                

This earth figure is isometry
b/c each half of the earth
is equal distance from
the other half. 

• The reason why dilation isn't a isometry is because the original image is either shrunk or enlarged. 

Example of  dilation, where
ΔABC is dilated by the
scale factor of 2.

• Now you try it, with this question :

What isometry maps figure 1 to figure 3?

Choices:

A.          reflection 

B.       translation 

C.            rotation 

D.  none of these