Each control has a
PointToScreen
method which you can use to convert the local coords that you have into screen coordinates that you can place your new form at. So from your original form you should be able to do something like this:
void textBox1_KeyDown(...)
{
Point newFormPos = this.PointToScreen(new Point(10,40));
newForm.Location = newFormPos;
newForm.Show();
}