Each Geometry has a specific CoordinateSystem which relates the coordinates of the geometry to locations on the earth. You can change a geometry to use a different CoordinateSystem by projecting it. All geometries drawn on the MapDisplay in ArcGIS Explorer automatically draw using the coordinate system of the display - this includes the geometries which are used to draw Graphics and all types of MapItem - you do not need to add any code for these items to be projected correctly.

However, if you wish to interact with other systems which require location or geometry input or output in a specific coordinate system, you can use the Project method in order to perform this work.

The ArcGIS Explorer application maintains a collection of GeographicTransformations in the GeographicTransformations2D and GeographicTransformations3D properties. Adding a GeographicTransformation to these collection ensures it will be used in a call to Project, and would also be used internally to project any layers or graphics on-the-fly, if those objects have an appropriate coordinate system pair. The collection used depends on whether the current DisplayMode is 2D or 3D.