When use matrixTransform zoom a line, the precision will lost

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WPF

I draw a polygon line with 100 points, the startPoint is (10.000001, 10.000001), the offset = 0.000001, the next point is plus the offset (10.000002, 10.000002), then I zoom the line to 1e6 times or more by matrixTransform, but I saw the the line is not a beeline, is a sawtooth line.
Why does it not work? Do you have any solution for this issue?

MoreInfo:
I draw the line in a coordinate system (x axis & y axis, like x axis range is the point.x's range, 10.000001~10.0001), and the points are the real data. I want to just draw it by the real points and by the matrixTransform to show the real line I needed.
A strange problem is, I transform the points by matrixTransform, and draw the line is not missing the precision. there is a simple demo for it.

Here is my code:
Xaml:

<Window x:Class="TestMatrix.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="MainWindow" Height="600" Width="700">
    <Grid x:Name="grid">
        <Grid.ColumnDefinitions>
            <ColumnDefinition Width="auto"/>
            <ColumnDefinition Width="auto"/>
        </Grid.ColumnDefinitions>
        <Canvas Background="Blue" x:Name="canvas" Width="300" Height="500" Margin="25">
            <Path Stroke="Red" x:Name="path">
                <Path.Data>
                    <PathGeometry x:Name="geometry">
                        <PathGeometry.Figures>
                            <PathFigure x:Name="pathFigure" >
                                <PathFigure.Segments>
                                    <PolyLineSegment x:Name="polyLineSegment" ></PolyLineSegment>
                                </PathFigure.Segments>
                            </PathFigure>
                        </PathGeometry.Figures>
                    </PathGeometry>
                </Path.Data>
            </Path>
        </Canvas>
        <Canvas x:Name="noMatrixCanvas" Grid.Column="1" Width="300" Height="500" Background="LightBlue">
            <Path Stroke="Red">
                <Path.Data>
                    <PathGeometry x:Name="geometryNo">
                        <PathGeometry.Figures>
                            <PathFigure x:Name="pathFigureNo" >
                                <PathFigure.Segments>
                                    <PolyLineSegment x:Name="polyLineSegmentNo" ></PolyLineSegment>
                                </PathFigure.Segments>
                            </PathFigure>
                        </PathGeometry.Figures>
                    </PathGeometry>
                </Path.Data>
            </Path>
        </Canvas>
    </Grid>
</Window>

CS:

private List<Point> m_listPoints = new List<Point>();
private int count = 100;
private double c_offset = 1e-7;
private MatrixTransform m_transform;
public MainWindow()
{
    InitializeComponent();
    InitPoints(count);
    DrawWithMatrix();
    DrawNoMatrixTransform();
}

private void DrawWithMatrix()
{
    pathFigure.StartPoint = m_listPoints[0];
    PolyLineSegment poly = new PolyLineSegment(m_listPoints, true);
    polyLineSegment.Points = poly.Points;

    m_transform = new MatrixTransform();
    m_transform.Matrix = GetMatrix(canvas, count);
    geometry.Transform = m_transform;
}

private void InitPoints(int count)
{
    double xValue = 4.989826;
    double yValue = 9.012345;
    for (int i = 0; i < count; i++)
    {
        m_listPoints.Add(new Point(xValue + i * c_offset, yValue + i * c_offset));
    }
}
private Matrix GetMatrix(FrameworkElement fe, int count)
{
    double scaleX = fe.Width / (count * c_offset);
    double scaleY = fe.Height / (count * c_offset);

    Matrix matrix = new Matrix();

    matrix.Translate(-m_listPoints[0].X, -m_listPoints[count - 1].Y);
    matrix.Scale(scaleX, -scaleY);

    return matrix;
}
private void DrawNoMatrixTransform()
{
    var realPoints = GetRealPoints();
    pathFigureNo.StartPoint = realPoints[0];
    PolyLineSegment poly = new PolyLineSegment(realPoints, true);
    polyLineSegmentNo.Points = poly.Points;
}

private List<Point> GetRealPoints()
{
    List<Point> pixelPoints = new List<Point>();
    m_listPoints.ForEach(point =>
    {
        //get realPoint by compute
        //double x = (point.X - m_listPoints[0].X) * noMatrixCanvas.Width / (count * c_offset);
        //double y = -(point.Y - m_listPoints[count - 1].Y) * noMatrixCanvas.Height / (count * c_offset);
        //pixelPoints.Add(new Point(x, y));

        //get realPoint by matrix
        Point realPoint = m_transform.Transform(point);
        pixelPoints.Add(realPoint);
    }
    );
    return pixelPoints;
}

Thanks
Weiqiang