protected virtual Task HandleMouseDownAsync( 
   MapViewMouseButtonEventArgs args
)

public ProSnippetMapTool()
{
  //Set the MapTool base class' OverlayControlID to the DAML id of your embeddable control in the constructor
  OverlayControlID = "ProAppModule1_EmbeddableControl1";
}

// Override the MapTool base class' OverlayControlPositionRatio property to set the position of the embeddable control
protected static void OnToolMouseDown(MapViewMouseButtonEventArgs e)
{
  if (e.ChangedButton == MouseButton.Left)
    e.Handled = true;
}

// Override the MapTool base class' HandleMouseDownAsync method to set the position of the embeddable control
protected static Task HandleMouseDownAsync(MapViewMouseButtonEventArgs e)
{
  return QueuedTask.Run(() =>
  {
    Point
          //assign the screen coordinate clicked point to the MapTool base class' OverlayControlLocation property.
          OverlayControlPositionRatio = e.ClientPoint;
  });
}

{
  //Note: Must be on QueuedTask.Run
  var pointSymbol = SymbolFactory.Instance.ConstructPointSymbol(ColorFactory.Instance.BlackRGB, 8);
  //Convert the clicked point in client coordinates to the corresponding map coordinates.
  //clicked point can be from a Map Tool's HandleMouseDownAsync callback.
  //MapViewMouseButtonEventArgs ClientPoint property.
  Point clickedPoint;
  var clickedMapPoint = MapView.Active.ClientToMap(clickedPoint);
  ArcGIS.Desktop.Framework.Dialogs.MessageBox.Show(string.Format("X: {0} Y: {1} Z: {2}",
      mapPoint.X, mapPoint.Y, mapPoint.Z), "Map Coordinates");
  //Get the corresponding layout point
  var pointOnLayoutFrame = mapFrame.MapToPage(mapPoint);

  //Create a point graphic on the Layout.
  var cimGraphicElement = new CIMPointGraphic
  {
    Location = pointOnLayoutFrame,
    Symbol = pointSymbol.MakeSymbolReference()
  };
  //Or use GraphicFactory
  var cimGraphicElement2 = GraphicFactory.Instance.CreateSimpleGraphic(
          pointOnLayoutFrame, pointSymbol);

  ElementFactory.Instance.CreateGraphicElement(layout, cimGraphicElement);
  ElementFactory.Instance.CreateGraphicElement(layout, cimGraphicElement2);
}

internal class GetMapCoordinates : MapTool
{
  protected override void OnToolMouseDown(MapViewMouseButtonEventArgs e)
  {
    if (e.ChangedButton == System.Windows.Input.MouseButton.Left)
      e.Handled = true; //Handle the event args to get the call to the corresponding async method
  }

  protected override Task HandleMouseDownAsync(MapViewMouseButtonEventArgs e)
  {
    return QueuedTask.Run(() =>
    {
      //Convert the clicked point in client coordinates to the corresponding map coordinates.
      var mapPoint = MapView.Active.ClientToMap(e.ClientPoint);
      ArcGIS.Desktop.Framework.Dialogs.MessageBox.Show(string.Format("X: {0} Y: {1} Z: {2}",
                  mapPoint.X, mapPoint.Y, mapPoint.Z), "Map Coordinates");
    });
  }
}