Java 2D: Moving a point P a certain distance closer to another point?

Question

What is the best way to go about moving a Point2D.Double x distance closer to another Point2D.Double?

Edit: Tried to edit, but so went down for maintenance. No this is not homework

I need to move a plane (A) towards the end of a runway (C) and point it in the correct direction (angle a).

alt text http://img246.imageshack.us/img246/9707/planec.png

Here is what I have so far, but it seems messy, what is the usual way to go about doing something like this?

    //coordinate = plane coordinate (Point2D.Double)
    //Distance = max distance the plane can travel in this frame

    Triangle triangle = new Triangle(coordinate, new Coordinate(coordinate.x, landingCoordinate.y),  landingCoordinate);

    double angle = 0;

    //Above to the left
    if (coordinate.x <= landingCoordinate.x && coordinate.y <= landingCoordinate.y)
    {
        angle = triangle.getAngleC();
        coordinate.rotate(angle, distance);
        angle = (Math.PI-angle);
    }
    //Above to the right
    else if (coordinate.x >= landingCoordinate.x && coordinate.y <= landingCoordinate.y)
    {
        angle = triangle.getAngleC();
        coordinate.rotate(Math.PI-angle, distance);
        angle = (Math.PI*1.5-angle);
    }

    plane.setAngle(angle);

The triangle class can be found at http://pastebin.com/RtCB2kSZ

Bearing in mind the plane can be in in any position around the runway point

Answer 1

The shortest distance between two points is a line, so simply move that point x units along the line that connects the two points.

---

Edit: I didn't want to give away the specifics of the answer if this is homework, but this is simple enough that it can be illustrated without being too spoiler-y.

Let us assume you have two points A = (x₁, y₁) and B = (x₂, y₂). The line that includes these two points has the equation

(x₁, y₁) + t · (x₂ - x₁, y₂ - y₁)

where t is some parameter. Notice that when t = 1, the point specified by the line is B, and when t = 0, the point specified by the line is A.

Now, you would like to move B to B', a point which is a new distance d away from A:

 A                       B'            B
(+)---------------------(+)-----------(+)

 <========={ d }=========>

The point B', like any other point on the line, is also governed by the equation we showed earlier. But what value of t do we use? Well, when t is 1, the equation points to B, which is |AB| units away from A. So the value of t that specifies B' is t = d/|AB|.

Solving for |AB| and plugging this into the above equation is left as an exercise to the reader.