8.01 Types of Transformations

Introduction

Maybe you have heard of the movie Transformers. Seeing complex mechanical objects transform into something totally cool is what makes the movie interesting. We may not have mechanical monsters from outer space in geometry class, but we do have transformations.

A transformation is how we manipulate a point, line, or geometric figure. The original shape of the object is called the pre-image and the final shape and position of the object is the transformation. In this unit, we will look at different types of transformation.

Do you remember doing constructions earlier in the course? We will be doing some in this lesson as well by learning how to define squares in circles, circles in squares, and triangles in both.

Using GeoGebra: ACCESS - Reflection, explore the images you can create. You can click any of the options on the left, then manipulate the black line by dragging it by the blue open points to move it. You can move the shapes using the green dragger points.

Try the experiments below.

Select a figure and drag the line to create two objects (the figure and its reflection).

1. Are the objects identical? If not, how do they differ?

2. How does the angle of the reflected figure to the line compare to the angle of the original figure to the line? (Hint - look at the dashed line)

Select a figure. Drag the line over the figure.

3. Can you make it so that the overlap between the original and reflected figure match the original figure completely? How?

4. Will this work for all figures? If not, can you explain how you can tell whether or not it will work?

Download, complete, and submit 8.01 Explore.