Calculate a point along the line A-B at a given distance from A

I'm going quite mad trying to calculate the point along the given line A-B, at a given distance from A, so that I can "draw" the line between two given points. It sounded simple enough at the outset, but I can't seem to get it right. Worse still, I don't understand where I've gone wrong. Geometry (and math in general) is NOT my strong suite.

I have read similar questions and there answers on SO. In fact I lifted my current implementation of CalculatePoint function directly from Mads Elvheim's answer to: Given a start and end point, and a distance, calculate a point along a line (plus a correction in a later comment - if I understand him correctly) because my indepedent attempts to solve the problem were getting me nowhere, except a first class express ticket frusterpationland.

Here's my UPDATED code (please see the EDIT notes a bottom of post):

using System;
using System.Drawing;
using System.Windows.Forms;

namespace DrawLines
{
    public class MainForm : Form
    {
        // =====================================================================
        // Here's the part I'm having trouble with. I don't really understand
        // how this is suposed to work, so I can't seem to get it right!
        // ---------------------------------------------------------------------

        // A "local indirector" - Just so I don't have go down and edit the 
        // actual call everytime this bluddy thing changes names.
        private Point CalculatePoint(Point a, Point b, int distance) {
            return CalculatePoint_ByAgentFire(a, b, distance);
        }

        #region CalculatePoint_ByAgentFire
        //AgentFire: Better approach (you can rename the struct if you need):
        struct Vector2
        {
            public readonly double X;
            p