Find new coordinates of point on line in javascript [closed]

Question

Let's say I have two points which I know: x1,y1 and x2,y2. I know I can easily calculate the length of this line with Pythagorean, but what if I want to calculate a shortened version of the line. For example, I would like the x,y coordinates 10 pixels toward the next point. Is there a simple formula for finding any new point on an angled line?

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OK, here is the solution as a JavaScript function. I've intentionally made this extra verbose for explanatory purposes. As the comments below suggested, you have to find the angle first, then calculate the sides with a new hypotenuse.

/**
 *  Calculates length of a line on Cartesian grid, then returns point that is X number of pixels down the line.
 *
 * @param  {Number} fromX - starting x point
 * @param  {Number} fromY - starting y point
 * @param  {Number} toX - ending x point for vector
 * @param  {Number} toY - ending y point for vector
 * @param  {Number} pxDistance - Number of pixels down line toward ending point to return
 * @return {Object} Returns x/y coords of point on line based on number of pixels given
 */ 
function stortenLineDistance(fromX, fromY, toX, toY, pxDistance){

    //if line is vertical
    if(fromX === toX)
        return {x: toX, y: toY > fromY ? fromY + pxDistance : fromY - pxDistance};

    //if line is horizontal
    if(fromY === toY)
        return {y: toY, x: toX > fromX ? fromX + pxDistance : fromX - pxDistance};

    //get each side of original triangle length
    var adjacent   = toY - fromY;
    var opposite   = toX - fromX;
    var hypotenuse = Math.sqrt(Math.pow(opposite, 2) + Math.pow(adjacent,2));

    //find the angle
    var angle = Math.acos(adjacent/hypotenuse);

    //calculate new opposite and adjacent sides
    var newOpposite = Math.sin(angle) * pxDistance;
    var newAdjacent = Math.cos(angle) * pxDistance;

    //calculate new x/y, see which direction it's going
    var y = fromY - newAdjacent,
        x = fromX + newOpposite;

    return {y: y, x: x};

}

EDIT: Wow, Stackoverflow is brutal. Feel free to delete this question if you wish, though I think it could be helpful to someone stuck on the same issue down the line. Maybe I'm wrong.

At any rate, thanks to commenters for help.

Answer 1

I've created a fiddle that utilizes a ratio of corresponding sides. Adjust variable smallerLen to any unit to see the point move across the line.

http://jsfiddle.net/3SY8v/