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Find two vertices of an isosceles triangle in which there is rectangle with opposite corners (0, 0) and (X, Y)

  • Last Updated : 22 Mar, 2021

Given two integers X and Y. The task is to find two vertices of an isosceles triangle ABC(right-angled at B) which has one vertex at a point B(0, 0). And there is a rectangle with opposite sides (0, 0) and (X, Y). All the points of this rectangle are located inside or on the border of the triangle. Print 4 integers x1, y1, x2, y2, where A(x1, y1) and B(x2, y2).
Examples: 
 

Input : X = 3, Y = 3 
Output : 6 0 0 6 
 

Input : X = -3, y = -2 
Output : -5 0 0 -5 
 



 

 

Approach : 
Let Val = |x| + |y|. Then the first point is (Val * sign(x), 0) and the second point is (0, Val * sign(y)). 
Let’s see how it works for x > 0 and y > 0. Other cases can be proved in a similar way. 
We need to show, that (x, y) belongs to our triangle(including its borders). In fact (x, y) belongs to segment, connecting (x + y, 0) with (0, x + y). The line through (x + y, 0) and (0, x + y) is Y = – X + x + y. Using coordinates (x, y) in this equation proves our answer.
Below is the implementation of the above approach: 
 

C++




// C++ program to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
#include <bits/stdc++.h>
using namespace std;
 
// Function to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
int Vertices(int x, int y)
{
    // Required value;
    int val = abs(x) + abs(y);
 
    // print x1 and y1
    cout << val * (x < 0 ? -1 : 1) << " 0 ";
 
    // print x2 and y3
    cout << "0 " << val * (y < 0 ? -1 : 1);
}
 
// Driver code
int main()
{
    int x = 3, y = 3;
 
    // Function call
    Vertices(x, y);
 
    return 0;
}

Java




// Java program to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
class GFG
{
 
// Function to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
static void Vertices(int x, int y)
{
    // Required value;
    int val = Math.abs(x) + Math.abs(y);
 
    // print x1 and y1
    System.out.print(val * (x < 0 ? -1 : 1) + " 0 ");
 
    // print x2 and y3
    System.out.print("0 " + val * (y < 0 ? -1 : 1));
}
 
// Driver code
public static void main(String[] args)
{
    int x = 3, y = 3;
 
    // Function call
    Vertices(x, y);
}
}
 
// This code is contributed by Rajput-Ji

Python3




# Python3 program to find two vertices of an
# isosceles triangle in which there is
# rectangle with opposite side (0, 0) and (x, y)
 
# Function to find two vertices of an
# isosceles triangle in which there is
# rectangle with opposite side (0, 0) and (x, y)
def Vertices(x, y) :
 
    # Required value;
    val = abs(x) + abs(y);
 
    # print x1 and y1
    if x < 0 :
        x = -1
    else :
        x = 1
         
    print(val * x,"0",end = " ");
 
    # print x2 and y3
    if y < 0 :
        y = -1
    else :
        y = 1
     
    print("0",val * y);
 
 
# Driver code
if __name__ == "__main__" :
 
    x = 3; y = 3;
 
    # Function call
    Vertices(x, y);
 
# This code is contributed by AnkitRai01

C#




// C# program to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
using System;
     
class GFG
{
 
// Function to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
static void Vertices(int x, int y)
{
    // Required value;
    int val = Math.Abs(x) + Math.Abs(y);
 
    // print x1 and y1
    Console.Write(val * (x < 0 ? -1 : 1) + " 0 ");
 
    // print x2 and y3
    Console.Write("0 " + val * (y < 0 ? -1 : 1));
}
 
// Driver code
public static void Main(String[] args)
{
    int x = 3, y = 3;
 
    // Function call
    Vertices(x, y);
}
}
 
// This code is contributed by Rajput-Ji

Javascript




<script>
 
// JavaScript program to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
 
// Function to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
function Vertices(x, y)
{
    // Required value;
    let val = Math.abs(x) + Math.abs(y);
 
    // print x1 and y1
    document.write(val * (x < 0 ? -1 : 1) + " 0 ");
 
    // print x2 and y3
    document.write("0 " + val * (y < 0 ? -1 : 1));
}
 
// Driver code
 
    let x = 3, y = 3;
 
    // Function call
    Vertices(x, y);
 
 
// This code is contributed by Surbhi Tyagi.
 
</script>
Output: 
6 0 0 6

 

Time Complexity : O(1)
 




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