Line mouse;
Line relative;
float angleDifference;

void setup(){
  size(200, 200);
  mouse = new Line(new Point(100,100), new Point(mouseX, mouseY));
  relative = new Line(mouse.a, new Point(100,0));
  // Here's how I figure out the angle my other line is away from the mouse
  angleDifference = relative.getTheta() - mouse.getTheta();
}

void draw(){
  background(255);
  stroke(0);
  line(mouse.a.x, mouse.a.y, mouse.b.x, mouse.b.y);
  stroke(255,0,0);
  line(relative.a.x, relative.a.y, relative.b.x, relative.b.y);
  mouse.b = new Point(mouseX, mouseY);
  mouse.updateLine();
  // And I just use trig to force the other line to be at the right angle away from the mouse
  float theta = angleDifference + mouse.getTheta();
  relative.b.x = relative.a.x + cos(theta) * relative.len;
  relative.b.y = relative.a.y + sin(theta) * relative.len;
  relative.updateLine();
}

static class Line{
  Point a, b;
  float vx, vy, dx, dy, lx, ly, rx, ry, len, invLen, theta;
  // Constructor
  Line(Point a, Point b){
    this.a = a;
    this.b = b;
    updateLine();
  }
  // Refresh values of normals
  void updateLine(){
    vx = b.x - a.x;
    vy = b.y - a.y;
    len = sqrt(vx * vx + vy * vy);
    if(len > 0){
	dx = vx/len;
	dy = vy/len;
    } else {
	dx = 0.0f;
	dy = 0.0f;
    }
    rx = -dy;
    ry = dx;
    lx = dy;
    ly = -dx;
  }
  // Get the angle of the line
  float getTheta(){
    theta = atan2(vy, vx);
    return theta;
  }
  // Return the dot product of two vectors (lines)
  static float dot(Line a, Line b){
    return a.vx * b.vx + a.vy * b.vy;
  }
}

static class Point{
  float x, y;
  // Constructor
  Point(float x, float y){
    this.x = x;
    this.y = y;
  }
}