use java the Checking the Types of Triangle

Requirements

Given a set of (x, y) coordinates representing the vertices of triangles, write a Java program to check the types of all the triangles formed by selecting any three given vertices. The following shows an example displaying all possible triangles formed from 6 vertices.

1. Write appropriate methods to do the following tasks, one method for each:

- Given the coordinates of the two vertices of a side of a triangle, calculate its length.

- Given the length of the three sides of a triangle, calculate its area.

- Given the length of the three sides of a triangle, check if it is a valid triangle.

- Given the length of the three sides of a triangle, check if it is right-angled.

- Given the length of the three sides of a triangle, check if it is isosceles.

- Given the length of the three sides of a triangle, check if it is scalene.

2. Input the coordinates of the vertices of triangles from a text file. Each row represents the (x, y) coordinates of a vertex of a triangle, and the two coordinate integers should be read into two integer array representing the x and y coordinates of all vertices. The last row (999, 999) is used to indicate end-of-file and should not be used as formal data.

An example input text file is shown below:

vertices.txt

-5 2

0 2

8 2

8 -11

4 2

4 5

999 999

3. Using appropriate iterations to select all the triangles formed by choosing any three vertices inputted in (1).

- For each triangle, check and display its types.

- Find and display the triangle with maximum area and the one with minimum area. The format of the maximum and minimum area is having 2 decimal places only.

the format of the output of the program is shown below

point1 point2 point 3 Types of Triangle

(-5,2) (0,2) (8,2) Non-triangle

(-5,2) (0,2) (8,-11) Scalene