Translate Coordinates Relative To Line Segment

I need to write a function (in Javascript) that accepts the endpoints of a line segment and an additional point and returns coordinates for the point relative to the start point. S

Solution 1:

I took a different approach, by combining two functions:

1. To get yp' I find the intersection point using the answer from here: Perpendicular on a line from a given point
2. To get xp' I calculate the distance between (xp, yp) and the line, using the equation from here: https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line

Not the most elegant solution, but it seems to work.

Resulting code https://jsfiddle.net/qke0m4mb/

functionperpendicular_coords(x1, y1, x2, y2, xp, yp) {
  var dx = x2 - x1,
      dy = y2 - y1;

  //find intersection point    var k = (dy * (xp-x1) - dx * (yp-y1)) / (dy*dy + dx*dx);
  var x4 = xp - k * dy;
  var y4 = yp + k * dx;

  var ypt = Math.sqrt((y4-y1)*(y4-y1)+(x4-x1)*(x4-x1));
  var xpt = distance(x1, y1, x2, y2, xp, yp);
  return [xpt, ypt];
}

// Distance of point from linefunctiondistance(x1, y1, x2, y2, xp, yp) {
  var dx = x2 - x1;
  var dy = y2 - y1;

  returnMath.abs(dy*xp - dx*yp + x2*y1 - y2*x1) / Math.sqrt(dy*dy + dx*dx);
}