(Geometry: the Triangle2D class) Define the Triangle2D class that contains:■ Three points...

(Geometry: the Triangle2D 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

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■ A no-arg constructor that creates a default triangle with the points (0, 0), (1, 1), and (2, 5).

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■ A constructor that creates a triangle with the specified points.

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■ A method getArea() that returns the area of the triangle.

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■ A method getPerimeter() that returns the perimeter of the triangle.

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■ A method contains(MyPoint p) that returns true if the specified point p is inside this triangle (see Figure 1a).

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■ A method contains(Triangle2D t) that returns true if the specified triangle is inside this triangle (see Figure 1b).

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■ A method overlaps(Triangle2D t) that returns true if the specified triangle overlaps with this triangle (see Figure 1c).

FIGURE 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 t1. overlaps(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 To detect whether a point is inside a triangle, draw three dashed lines, as shown in Figure 2. 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)

FIGURE 2 (a) A point is inside the triangle. (b) A point is outside the triangle.