Day 1 : Exploring Transformations
by Jongsuk Keum
Before learning a formal definition of each translation, rotation, reflection,
glide reflection, and dilation, students explore 5 types of transformation
using GSP. The GSP is very useful tool for the students to grasp the meaning
of translation, rotation, reflection, glide reflection, and dilation.
Write a "lab report" on the Geometer's Sketchpad transformations
Translate, Rotate, and Reflect. Using words and pictures, explain what each
of these three transformations does.
Here are some questions you may want to address for
each type of transformation:
- Can you give a physically
intuitive description of the transformation?
- What data is needed
to define the transformation?
- What geometrical properties
does the transformation have?
Can you define geometrically
exactly what the transformation does?
* Translations can be described intuitively as
slide. Given any geometric object, such as a point, a line, a disk,
etc, on the plane or on a table, sliding the object, we obtain the translated
image. Vectors can characterize translations.
* Turn is the physical and intuitive representation
of a rotation. A wheel,
geometrically a circle with a center, can best describe a rotation.
* Flip is the physical and intuitive representation
of a rotation. Reflections can
be observed in several events in everyday life:
mirror, decalcomania, etc. They can be best
described intuitively and
physically by mirrors. The mirrors will play the role of the reflection
and images on the mirrors are reflected images. We all experienced how
beautiful the decalcomania was when we carried it out for the very first
time in a pre-kindergarten class.
Give mathematical definitions of the three types
of transformations we have been studying : reflection, glide reflection,
rotation, and translation.
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