We shall now look at what happens to polygons under reflections. As before, you click on Draw and then several 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 line segments. 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:
Where do you have to place a line segment so that the line segment and its image are on the same line?
Where do you have to place a line segment so that the line segment and its image are parallel?
Where do you have to place a line segment so that the line segment and its image are perpendicular?
If the mirror line is the line y = x and 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 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 reflection?
e-mail: C. Mawata