Having seen what happens to a point under a translation, we shall now look at what happens to other geometric figures. The applet will allow you to draw polygons.
To get used to the applet, click on the On/Off button and then on the Draw button. Now click a few times on the graph paper to draw a polygon. Each time you click on the Draw button you can draw a new polygon. If it gets crowded click on the Clear button.
Let us start with a line segment. You can get one by clicking at the locations of the endpoints. Notice that if the object is a line segment then the image is also a line segment. Experiment until you can answer the following questions:
If a line segment has endpoints (a,b) and (c,d), which two translation vectors will position the image so that the line segments are end to end?
If you are given that the translation vector is (r,s) and that the object is a line segment with endpoints (a,b) and (c,d), what are the endpoints of the image?
Is it ever possible for the image of a line segment to be perpendicular to the object?
Is it ever possible for the image of a line segment to be longer or shorter than the object?
Do a few experiments with triangles, quadrilaterals, and other polygons. Which geometric properties (e.g. sizes of angles, areas etc.) seem to be preserved under translation?
e-mail: C. Mawata