**TASK**

This might look like a rather technical and daunting task. It might also seem rather contrived, in that it relies on a specific, and particularly nice configuration, the 30˚60˚90˚ triangle. However, it is not vital that the task is solved in every detail - its prime purpose is to provide an opportunity to **explore the properties of a shear**.

The shear is a geometric transformation that will be relatively unfamiliar to many students and teachers. It is an **affine** transformation, as are the more familiar translation, rotation, reflection and enlargement.

Some properties of a shear are listed below; if they appear rather dry, then running the movies and exploring the JAVA worksheets that can be found on these pages should help give meaning to them:

A shear of the plane is defined by an **invariant line** and a **shear factor**;

all points in the plane move parallel to the invariant line;

the distance a point moves depends on the value of the shear factor and is directly proportional to the point's distance from the invariant line;

a shear preserves area;

straight lines remain straight;

parallel lines remain parallel.

We start by showing the effect of the shear *M* on the square ABCD: NEXT PAGE

FREE:

a high-res pdf file of this new GEOaa-zz task

a high-res pdf file of this new GEOaa-zz task