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);
}
}
```