Creating coordinates on the form?

Use simple mathematics. You must store your original 0,0 point location on form. Assuming your form has dimensions: 300x200 and you have your axis exactly in the middle of the form you can do like this:

private int X0 = 150;
private int Y0 = 100;

// Pass your values to calculation method
private Point CalculatePoint(int x, int y)
{
    return new Point(X0 + x, Y0 + y);
}

Then in your code you call this method like this:

var point1 = CalculatePoint(2, 3);    // 152, 103
var point2 = CalculatePoint(-4, 5);   // 146, 105
var point3 = CalculatePoint(-5, -7);  // 145, 93
var point4 = CalculatePoint(4, -6);   // 154, 94

You can use form's OnClientSizeChanged to determine when form size changed. Then simply update your original point location:

private void Form1_ClientSizeChanged(object sender, EventArgs e)
{
    X0 = this.Size.Width / 2;
    Y0 = this.Size.Height / 2;
}

And don't forget to redraw your chart.

Cheers!