KB10798 - What is the best way using the DK to rotate, scale, or move a shape to a new position?

The recommended way to rotate, scale, or move a selected shape is to use the TGIS_Shape.Transform function. This function will transform the shape based on parameters specified by matrix and translation vector.

Refer to http://en.wikipedia.org/wiki/Rotation_(mathematics) and http://en.wikipedia.org/wiki/Transformation_matrix for the mathematical background of the Transform operation.