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**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.