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Transformations & Symmetry

What is transformation?Transformation is a one-to-one function from one plane on to
another plane or to a different area on the same plane.A transformation describes a change in
appearance of points in a plane.It is a transfer from the pre-image to the image.There are
many types of transformations that I will be describing.
Thefirst type of transformation is known as a reflection.A reflection maps each point
from one plane and creates it on another plane in the same manner and order.One of the main
characteristics of reflection is reverse orientation.This means that whatever order the points
were in, they transformed to be the opposite.This concept is the same as when you look into a
mirror, all the points are reversed.
Another type of transformation is known as translation.A translation is a transformation
formed by the composition of two reflections in which the lines of the reflection are parallel.
According to my understanding of this concept, in order to have the lines parallel, the figures
must be placed side by side.In this type of transformation the orientation of the figure is
changed but then changed back.Thefirst reflection reverses the orientation, then the second
reflection reverses it back to the way itfirst was.When you have more than one transformation
of one figure you are then, performing a composition of transformations.
The third type of translation is called a rotation.A rotation is a transformation formed
by the composition of two reflections in which the lines of reflection intersect.This is
accomplished by using two reflections or a composition.The concept of this transformation is
that it is reflected at an angle, therefore causing the perpendicular lines to intersect at a single
Another type of transformation is known as a dilation.A dilation is kn

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