// represents an abstract shape
abstract class AShape {
 CartPt loc;





 // to compute the area of this shape
 abstract double area();


 // to compute the distance of
 // this shape to the origin
 abstract double distTo0();

 // is the given point within
 // the bounds of this shape
 abstract boolean in(CartPt p);




 // compute the bounding box
 // for this square
 abstract Square bb();
}

//represents a square (this.loc at top left)
class Square extends AShape {
 int size;

 Square(CartPt loc, int size) { 
  ... // omitted 
 }

 double area() {
  return this.size * this.size;
 }
 
 double distTo0() {
  return this.loc.distTo0();
 }

 boolean in(CartPt p){
  return 
   this.inRange(this.loc.y, p.y, this.size)
   && 
   this.inRange(this.loc.x, p.x, this.size);
 }

 Square bb() {
   return this;
 }

 // is x in the interval [lft,lft+wdth]?
 boolean inRange(int lft, int x, int wdth) {
  return lft <= x && x <= lft + wdth;
 }
}

class CartPt {
 int x;
 int y;

 CartPt(int x, int y) { ... // omitted ... }

 // to compute the distance of this point to the origin
 double distTo0(){
   return Math.sqrt( (this.x * this.x) + (this.y * this.y));
 }

 // compute the distance inRange this CartPt and p
 double distanceTo(CartPt p){
   return 
    Math.sqrt((this.x - p.x) * (this.x - p.x) + (this.y - p.y) * (this.y - p.y));
 }

 // create a new point that is deltaX, deltaY off-set from this point
 CartPt translate(int deltaX, int deltaY) { 
  return new CartPt(this.x + deltaX, this.y + deltaY);
 }
}