Open In App

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

Improve
Improve
Like Article
Like
Save
Share
Report

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)

Auxiliary Space: O(1)
 



Last Updated : 31 May, 2022
Like Article
Save Article
Previous
Next
Share your thoughts in the comments
Similar Reads