ArcGIS Pro 2.8 API Reference Guide
Rotate Method (IGeometryEngine)
Example 

ArcGIS.Core.Geometry Namespace > IGeometryEngine Interface : Rotate Method
The geometry to rotate.
The origin around which the geometry will be rotated.
The rotation angle in radians.
Rotates the geometry about the specified origin point.
Syntax

Parameters

geometry
The geometry to rotate.
origin
The origin around which the geometry will be rotated.
rotationAngle
The rotation angle in radians.

Return Value

The rotated geometry.
Exceptions
ExceptionDescription
Either geometry or origin or both are null or empty.
The method is not implemented for GeometryBag.
Incompatible spatial references between the input geometries.
Example
MapPoint pt = MapPointBuilder.CreateMapPoint(1.0, 3.0);
MapPoint rotatePt = MapPointBuilder.CreateMapPoint(3.0, 3.0);

Geometry result = GeometryEngine.Instance.Rotate(pt, rotatePt, Math.PI / 2);
// result point is (3, 1)
// rotate a polyline

MapPoint fixedPt = MapPointBuilder.CreateMapPoint(3.0, 3.0);

List<MapPoint> pts = new List<MapPoint>();
pts.Add(MapPointBuilder.CreateMapPoint(1.0, 1.0));
pts.Add(MapPointBuilder.CreateMapPoint(1.0, 5.0));
pts.Add(MapPointBuilder.CreateMapPoint(5, 5));
pts.Add(MapPointBuilder.CreateMapPoint(5.0, 1.0));
Polyline polyline = PolylineBuilder.CreatePolyline(pts);

Polyline rotated = GeometryEngine.Instance.Rotate(polyline, fixedPt, Math.PI / 4) as Polyline;  // rotate 45 deg
Requirements

Target Platforms: Windows 10, Windows 8.1

See Also

Reference

IGeometryEngine Interface
IGeometryEngine Members