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?

I.

* 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.

* Turn is the physical and intuitive representation
of a rotation. A wheel,

geometrically a circle with a center, can best describe a rotation.

III.

* 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.

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

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