java

10.12 (Geometry: the Triang e2D class) Define the Triangle2D class that contains: - Three points named p1, p2, and p3 of the type MyPoint with getter and setter methods. MyPoint is defined in Programming Exercise 10.4. - A no-arg constructor that creates a default triangle with the points (0,0),(1, 1), and (2,5). - A constructor that creates a triangle with the specified points. A method getArea() that returns the area of the triangle. - A method getPerimeter() that returns the perimeter of the triangle. A method contains (MyPoint p) that returns true if the specified point p is inside this triangle (see Figure 10.22a). A method contains (Triangle2D t) that returns true if the specified triangle is inside this triangle (see Figure 10.22b). A method over aps (Triangle2D t ) that returns true if the specified triangle overlaps with this triangle (see Figure 10.22c ). (a) (b) (c) Ficure 10.22 (a) A point is inside the triangle. (b) A triangle is inside another triangle. (c) A triangle overlaps another triangle. Draw the UML diagram for the class and then implement the class. Write a test program that creates a Triangle2D objects t1 using the constructor new Triangle2D (new MyPoint (2.5,2), new MyPoint (4.2,3), new MyPoint (5,3.5)), displays its area and perimeter, and displays the result of t1. contains ( 3 , 3), r1. contains(new Triangle2D (new MyPoint (2.9,2), new MyPoint (4,1), MyPoint (1,3.4)) ), and 1. over]aps (new Triangle2D (new MyPoint (2, 5.5), new MyPoint (4, -3). MyPoint (2,6.5)). (Hint: For the formula to compute the area of a triangle, see Programming Exercise 2.19. To detect whether a point is inside a triangle, draw three dashed lines, as shown in Figure 10.23. If the point is inside a triangle, each dashed line should intersect a side only once. If a dashed line intersects a side twice, then the point must be outside the triangle. For the algorithm of finding the intersecting point of two lines, see Programming Exercise 3.25.) FIGURE 10.23 (a) A point is inside the triangle. (b) A point is outside the triangle. 10.12 (Geometry: the Triang e2D class) Define the Triangle2D class that contains: - Three points named p1, p2, and p3 of the type MyPoint with getter and setter methods. MyPoint is defined in Programming Exercise 10.4. - A no-arg constructor that creates a default triangle with the points (0,0),(1, 1), and (2,5). - A constructor that creates a triangle with the specified points. A method getArea() that returns the area of the triangle. - A method getPerimeter() that returns the perimeter of the triangle. A method contains (MyPoint p) that returns true if the specified point p is inside this triangle (see Figure 10.22a). A method contains (Triangle2D t) that returns true if the specified triangle is inside this triangle (see Figure 10.22b). A method over aps (Triangle2D t ) that returns true if the specified triangle overlaps with this triangle (see Figure 10.22c ). (a) (b) (c) Ficure 10.22 (a) A point is inside the triangle. (b) A triangle is inside another triangle. (c) A triangle overlaps another triangle. Draw the UML diagram for the class and then implement the class. Write a test program that creates a Triangle2D objects t1 using the constructor new Triangle2D (new MyPoint (2.5,2), new MyPoint (4.2,3), new MyPoint (5,3.5)), displays its area and perimeter, and displays the result of t1. contains ( 3 , 3), r1. contains(new Triangle2D (new MyPoint (2.9,2), new MyPoint (4,1), MyPoint (1,3.4)) ), and 1. over]aps (new Triangle2D (new MyPoint (2, 5.5), new MyPoint (4, -3). MyPoint (2,6.5)). (Hint: For the formula to compute the area of a triangle, see Programming Exercise 2.19. To detect whether a point is inside a triangle, draw three dashed lines, as shown in Figure 10.23. If the point is inside a triangle, each dashed line should intersect a side only once. If a dashed line intersects a side twice, then the point must be outside the triangle. For the algorithm of finding the intersecting point of two lines, see Programming Exercise 3.25.) FIGURE 10.23 (a) A point is inside the triangle. (b) A point is outside the triangle