C# Program to Return Quadrant in which the Coordinate Lie

Cartesian-coordinate System and Quadrants

The cartesian-coordinate system is divided into four Quadrants: Quadrant I, Quadrant II, Quadrant III, and Quadrant IV. In this article, we are going to learn how we can determine the quadrant in which given points i.e., x and y, lie in C#.

Problem Description

We are given the position of a point (x, y), and we have to determine in which quadrant the given point lies in C#.

Example 1

• Input: (-6, 4)
• Output: Quadrant II

Example 2

• Input: (1, 2)
• Output: Quadrant I

Example 3

• Input: (4, -3)
• Output: Quadrant IV

Example 4

• Input: (-9, -2)
• Output: Quadrant III

Using Conditional Quadrant Identification Approach 

In this approach, we use if-else conditions to determine the quadrant in which given points lie. Below are the conditions to determine the quadrant in which the given point lies:

If >x > 0 and >y > 0, the given point lies in Quadrant I.
If >x < 0 and >y > 0, the given point lies in Quadrant II.
If >x < 0 and >y < 0, the given point lies in Quadrant III.
If >x > 0 and >y < 0, the given point lies in Quadrant IV.
If >x == 0 and >y != 0, the given point lies on the y-axis.
If >x != 0 and >y == 0, the given point lies on the x-axis.
If >x == 0 and >y == 0, the given point lies on the origin.

Implementation Code 

using System;

class Program {
  // Function to determine the quadrant of a point
  static string FindQuadrant(int x, int y) {
    if (x > 0 && y > 0) {
      return "Quadrant I";
    } else if (x < 0 && y > 0) {
      return "Quadrant II";
    } else if (x < 0 && y < 0) {
      return "Quadrant III";
    } else if (x > 0 && y < 0) {
      return "Quadrant IV";
    } else if (x == 0 && y != 0) {
      return "On the y-axis";
    } else if (x != 0 && y == 0) {
      return "On the x-axis";
    } else {
      return "At the origin";
    }
  }

  static void Main(string[] args) {
    int x = 7;
    int y = -3;

    Console.WriteLine($"The point ({x}, {y}) lies in {FindQuadrant(x, y)}");
  }
}

Output

The point (7, -3) lies in Quadrant IV

Time Complexity: O(1), constant time
Space Complexity: O(1), constant space

Using Ternary Operator 

The logic of this approach is the same as that of the above approach. We are going to use a ternary operator in this approach. In this approach, we use the ternary operator to determine the quadrant in which given points lie. The ternary operator (>? :) evaluates conditions in a nested structure.

Implementation Code 

using System;

class Program {
  static string FindQuadrant(int x, int y) {
    return (x > 0 && y > 0) ? "Quadrant I" : 
           (x < 0 && y > 0) ? "Quadrant II" : 
           (x < 0 && y < 0) ? "Quadrant III" : 
           (x > 0 && y < 0) ? "Quadrant IV" : 
           (x == 0 && y != 0) ? "On the y-axis" : 
           (x != 0 && y == 0) ? "On the x-axis" : 
           "At the origin";
  }

  static void Main(string[] args) {
    int x = 7;
    int y = -3;
    Console.WriteLine($"The point ({x}, {y}) lies in {FindQuadrant(x, y)}");
  }
}

Output

The point (7, -3) lies in Quadrant IV

Time Complexity: O(1), constant time
Space Complexity: O(1), constant space