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

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 ## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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 `

Output:

```6 0 0 6
```

Time Complexity : O(1)

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Improved By : AnkitRai01, Rajput-Ji