Day 1 : Exploring Transformations with GSP

by Jongsuk Keum

Goal

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.

Activity

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?

I. Translation

* 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.

II. Rotation

* Turn is the physical and intuitive representation of a rotation. A wheel,
geometrically a circle with a center, can best describe a rotation.

III. Reflection

* 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 line
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.

Homework

Give mathematical definitions of the three types of transformations we have been studying : reflection, glide reflection, rotation, and translation.

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