Geometry as Transformations
We will be exploring transformations because certain properties with complex numbers can be explain using geometry, specifically transformations. Transformations are when we move a figure in any way where we do not change the length of the figure itself. An image before and after a transformation is called a pre-image and an image.
We will be exploring transformations because certain properties with complex numbers can be explain using geometry, specifically transformations. Transformations are when we move a figure in any way where we do not change the length of the figure itself. An image before and after a transformation is called a pre-image and an image.
Isometries are transformations that do not change the length of a geometric figure. Isometries of the plane include rotation, translation, and reflection.
- Rotation is performed about a certain point and it transforms an object at the desired angle along the path of a circle. See Figure 6 [8].
- Here the figure ABCDE is rotated about the point F. The length from CF to C'F is of the same length since rotation from the point F produces the same figure with the same lengths and angles.
- Translation is motion along a vector. For example of translation see Figure 7 [8].
- Here the figure is being translated across a certain vector. Translation can be seen as sliding so the figure is being slided to the right a distance of 8 cm and with π radians.
- Reflection is a transformation that mirrors a geometric figure across a certain axis See Figure 8 [8].
- The figure with vertexes C, D, E, F, and G is being reflected across the line AB to form C' , D' , E' , F' , and G' . The line of reflection forms a perpendicular bisector across the line AB .