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: How do we graph dilations?

• Dilation is another main function of the transformations. Dilation: 

                      - is the ratio of an image or figure shrinks or enlarges from its original state of being [original size]. This is also known as a Scale Factor.

This is an example of dilation,
b/c the magnifying glass is making
the print look much bigger
through it's lens.

• When it comes to graphing dilations, you have to look at the Scale Factor. 

          

In this image ΔABC is dilated
 bigger to form ΔA'B'C'.
This shows that the scale
factor is bigger than 1. 

*Hint:

                      -If the scale factor is larger than 1, the image 

                        or figure has been enlarged [made bigger].

                       -If the scale factor is greater than 0 and less than 1, 

                   the image or figure has been shrinked. 

• When you're trying to solve any problem that has given you the ratio (scale factor) and original image, you multiply the ratio to the points given. 

An example of dilation in
real life. When  a  person is
excited or scared, their muscles
in their eyeballs stretch.