You could have a view model like the one shown below. Besides the obvious parts, it attaches/detaches a PropertyChanged handler to/from each Vertex in order to fire the PropertyChanged event for the Vertices property. This is necessary to update the Polyline's Point Binding.
public class ViewModelBase : INotifyPropertyChanged
{
    public event PropertyChangedEventHandler PropertyChanged;
    protected void OnPropertyChanged([CallerMemberName] string propertyName = null)
    {
        PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));
    }
}
public class Vertex : ViewModelBase
{
    private Point point;
    public Point Point
    {
        get { return point; }
        set { point = value; OnPropertyChanged(); }
    }
}
public class ViewModel : ViewModelBase
{
    public ViewModel()
    {
        Vertices.CollectionChanged += VerticesCollectionChanged;
    }
    public ObservableCollection<Vertex> Vertices { get; }
        = new ObservableCollection<Vertex>();
    private void VerticesCollectionChanged(
        object sender, NotifyCollectionChangedEventArgs e)
    {
        if (e.Action == NotifyCollectionChangedAction.Add)
        {
            foreach (var item in e.NewItems.OfType<INotifyPropertyChanged>())
            {
                item.PropertyChanged += VertexPropertyChanged;
            }
        }
        else if (e.Action == NotifyCollectionChangedAction.Remove)
        {
            foreach (var item in e.OldItems.OfType<INotifyPropertyChanged>())
            {
                item.PropertyChanged -= VertexPropertyChanged;
            }
        }
        OnPropertyChanged(nameof(Vertices));
    }
    private void VertexPropertyChanged(object sender, PropertyChangedEventArgs e)
    {
        OnPropertyChanged(nameof(Vertices));
    }
}
The Vertices to PointCollection converter could look like this:
public class VerticesConverter : IValueConverter
{
    public object Convert(
        object value, Type targetType, object parameter, CultureInfo culture)
    {
        var vertices = value as IEnumerable<Vertex>;
        return vertices != null
            ? new PointCollection(vertices.Select(v => v.Point))
            : null;
    }
    public object ConvertBack(
        object value, Type targetType, object parameter, CultureInfo culture)
    {
        throw new NotSupportedException();
    }
}
The view would use a Polyline and an ItemsControl. The ItemsTemplate would declare a Thumb element that handles the dragging of vertex points.
<Canvas>
    <Canvas.Resources>
        <local:VerticesConverter x:Key="VerticesConverter"/>
        <Style x:Key="ThumbStyle" TargetType="Thumb">
            <Setter Property="Template">
                <Setter.Value>
                    <ControlTemplate TargetType="Thumb">
                        <Rectangle Fill="Transparent" Stroke="Red"
                                   Width="10" Height="10" Margin="-5,-5"/>
                    </ControlTemplate>
                </Setter.Value>
            </Setter>
            <EventSetter Event="DragDelta" Handler="ThumbDragDelta"/>
        </Style>
    </Canvas.Resources>
    <Polyline Points="{Binding Vertices, Converter={StaticResource VerticesConverter}}"
              Stroke="DarkBlue" StrokeThickness="3" StrokeLineJoin="Round"/>
    <ItemsControl ItemsSource="{Binding Vertices}">
        <ItemsControl.ItemsPanel>
            <ItemsPanelTemplate>
                <Canvas/>
            </ItemsPanelTemplate>
        </ItemsControl.ItemsPanel>
        <ItemsControl.ItemContainerStyle>
            <Style TargetType="ContentPresenter">
                <Setter Property="Canvas.Left" Value="{Binding Point.X}"/>
                <Setter Property="Canvas.Top" Value="{Binding Point.Y}"/>
            </Style>
        </ItemsControl.ItemContainerStyle>
        <ItemsControl.ItemTemplate>
            <DataTemplate>
                <Thumb Style="{StaticResource ThumbStyle}"/>
            </DataTemplate>
        </ItemsControl.ItemTemplate>
    </ItemsControl>
</Canvas>
Finally, the Thumb's DragDelta handler:
private void ThumbDragDelta(object sender, DragDeltaEventArgs e)
{
    var vertex = (Vertex)((Thumb)sender).DataContext;
    vertex.Point = new Point(
        vertex.Point.X + e.HorizontalChange,
        vertex.Point.Y + e.VerticalChange);
}