A. Introduction If you observe the triangle.java in 8.6 carefully, the repetition of x and y coordinates of each vertex almost makes you to ask: is it possible to include a Vertex or Point class as a member of the Triangle class? private int Ax; 
 private int Ay; 
 private double ABlength; 
 private int Bx; 
 private int By; 
 private double BClength; 
 private int Cx; 
 private int Cy; 
 private double CAlength; The answer is YES. Not only as instance members, but also as static members as necessary. This is called class inclusion, as shown below: public class Point {
 double x; 
 double y;
 public Point(){ //empty constructor 
 }
 public Point(double i, double k){ //full constructor
 this.x = i; //use i & k because the formal parameters are general and hold no importance to code
 this.y = k;
 }
 public double getX(){ //getter or accessor
 return x;
 }
 public void setX(double i){ //setter or mutator
 x = i;
 }
 public double getY(){ //getter
 return y;
 }
 public void setY(double k){ //setter
 y = k;
 } 
 public double distance (Point aPoint){
 return Math.sqrt(Math.pow(this.x-aPoint.x,2)+Math.pow(this.y-aPoint.y,2));
 }
 
 public String toStr(){ // it is NOT called by System.out.println() by default
 return "(" + x + ", " + y +")";
 } 
 public String toString(){ // it is called by System.out.println() by default
 return "(" + x + ", " + y +")";
 } 
 public boolean equals(Point p){ // to compare two Point objects
 return p.x==x&&p.y==y;
 }
 
}

class TriangleByVertex {
 Point a;
 Point b;
 Point c;
 
 public double perimeter() {
 return a.distance(b)+b.distance(c)+c.distance(a); 
 }
 public double area() {
 double s = 0.5 * perimeter();
 return Math.sqrt(s*(s-side(b,c))*(s-side(a, c))*(s-side(a, b))); 
 }
 public double side(Point x, Point y){
 return x.distance(y);
 }
 
 public double angle(Point x){
 double cos;
 if(x.equals(a)) // use equals() method of Point class to check if two points are the same
 cos=(side(a,b)*side(a,b)+side(a,c)*side(a,c)-side(b,c)*side(b,c))/(2*side(a,b)*side(a,c));
 else if(x.equals(b)) 
 cos=(side(b,c)*side(b,c)+side(a,b)*side(a,b)-side(a,c)*side(a,c))/(2*side(b,c)*side(a,b));
 else if(x.equals(c))
 cos=(side(a,c)*side(a,c)+side(b,c)*side(b,c)-side(b,a)*side(b,a))/(2*side(a,c)*side(b,c));
 else {
 System.out.println("This vertex does not below the triangle!");
 return -1;
 }
 return Math.acos(cos);
 }
}
