TASK intro

The task can be approached deductively, using known properties of the isometries:
two 90˚ rotations of the plane are equivalent to a rotation of 180˚; the centre of this rotation is an 'invariant point'.
However, we are going to consider two empirical approaches, A and B:
in A, we apply the two transformations to a single object or set of objects (a triangular flag or flags), to see what happens;
in B, we apply the two transformations to various points in the plane and look for the point that returns to its starting position.