Transformations are the process in which an object's position is changed. The most common geometric transformations are translations, reflections, rotations and dilations. These transformations allow the complete manipulation of an object on the Cartesian plane. Examples of transformations can commonly be seen in daily life. Take a moment to look around at any point, place or time and it becomes evident how much geometric transformations effect and can be found in society and throughout the world. All that is needed to see these transformations is education in geometry transformations and an observant eye and curious mind. To assist others in their understanding of the importance of geometric mathematics and how important it is to everyday life, a baseline of definitions of translations, reflections, rotations and dilations is needed.
We will be exploring the properties and process of translations, reflections, rotations and dilations through their respective tabs in the menu bar above. But before we venture further into geometric transformations lets define some vocabulary. Knowing the vocabulary for geometric transformations helps establish a baseline of understanding of which further exploration with the transformations can begin.
The vocabulary defined in the table are important to know for the geometetric trnasformations as a whole, however there will be more specific vocabulary defined for the individual transformations as an additional resource while learning of these geometric transformations.
Defining Vocabulary
Vocabulary
Definition
Transformations
Transformations are a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.
Rigid Transformations
A rigid transformation is a transformation that does not alter the size or shape of a figure
Cartesian Plane
A Cartesian plane is made up of two perpendicular lines known as the x-axis (horizontal) and the y-axis (vertical). We can describe any point on this plane through a pair of ordered numbers found using the x and y axes.
A' ("A prime)
A', "A prime", denotes the transformed object's points from the original object. The label A' may be changed to label any point, using the letters of the alphabet. For example, B', C' and so on.
For a quick review of geometric transformations feel free to visit the following websites.