Question

Use SELECTION, DO NOT USE METHODES AND ARRAYS.

(Inside The Triangle)
Suppose a right triangle is placed in a plane as shown in the book. The right-angle point is placed at (0, 0), and the
other two points (x,y) are placed at (200, 0), and (0, 100). Write a program that prompts the user to enter a point with
x- and y-coordinates and determines whether the point is inside the triangle.

*** Methods are not allowed for this assignment. Do each calculation in the main.

Here is the equation for finding the area of a triangle.

abs((x1*(y2-y3) + x2*(y3-y1)+ x3*(y1-y2))/ 2.0 );

Here is some pseudocode that may help.

check whether the point P(10, 15)

           lies inside the triangle formed by  

           A(200, 0), B(0, 100) , C(0, 0) , P(userInputX,userInputY)

Calculate area of triangle ABC

Calculate area of triangle PBC

Calculate area of triangle PAC  

Calculate area of triangle PAB   

Check if sum of PBC, PAC and PAB is same as ABC

SAMPLE RUN #1: java InsideTheTriangle  

Enter a point's x and y coordinates: 200 0↵
The point is in the triangle↵

SAMPLE RUN #2: java InsideTheTriangle  

Enter a point's x and y coordinates: 900 0↵
The point is NOT in the triangle↵

PLEASE SELECTIONS, DONOT USE ARRAYS AND METHODES .

Answer 1

import java.util.Scanner;
public class InsideTheTriangle
{
public static void main(String[] args)
{
    //declare three points
    int x1=200,y1=0,x2=0,y2=100,x3=0,y3=0;
    Scanner input=new Scanner(System.in);
    System.out.print("Enter a point's x and y coordinates: ");
    int px=input.nextInt();
    int py=input.nextInt();
    //calculate area of triangle ABC
    double area1=Math.abs((x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2))/2.0);
    //calculate area of triangle PBC
    double area2=Math.abs((px*(y2-y3)+x2*(y3-py)+x3*(py-y2))/2.0);
     //calculate area of triangle PAC
    double area3=Math.abs((px*(y1-y3)+x1*(y3-py)+x3*(py-y1))/2.0);
     //calculate area of triangle PAB
    double area4=Math.abs((px*(y1-y2)+x1*(y2-py)+x2*(py-y1))/2.0);
    if(area1==area2+area3+area4)
    System.out.println("The point is in the triangle");
    else
    System.out.println("The point is NOT in the triangle");
}
}

Output