Double-click on the movie to PLAY.

Click once to PAUSE.

Find shear

In this movie we construct the invariant line and then apply the shear to A. It is worth pausing the movie periodically.

We start by finding an invariant point - namely the point where the line through the 'stem' of F and its image intersect.
The invariant line is a line through this point, parallel to the direction in which points in the plane (eg on F) move.

We can now determine that the shear factor is 1. [Pause the movie: notice that the distance a point moves is equal to its distance from the invariant line.]
We now use this factor to determine how far points on A move, parallel to the invariant line.

It is worth looking at the final image in detail. Note, for example,
• that just as F and A 'sit' on a staight line, so do their images;
• that the extension of any line segment and its image will intersect on the invariant line;
• that the horizontal line segments that are part of F and A remain parallel (or colinear).

On the next page we use a more static approach.