C# Program to Return Quadrant in which the Coordinate Lie

The Cartesian coordinate system is divided into four quadrants based on the signs of x and y coordinates. In this article, we will learn how to determine which quadrant a given point lies in using C#.

Understanding Quadrants

The coordinate plane is divided into four regions called quadrants

• Quadrant I: x > 0 and y > 0 (both positive)
• Quadrant II: x 0 (x negative, y positive)
• Quadrant III: x
• Quadrant IV: x > 0 and y

Problem Examples

• Input: (1, 2) ? Output: Quadrant I
• Input: (-6, 4) ? Output: Quadrant II
• Input: (-9, -2) ? Output: Quadrant III
• Input: (4, -3) ? Output: Quadrant IV

Using Conditional Statements

This approach uses if-else conditions to determine the quadrant. We also handle special cases where points lie on axes or at the origin

if (x > 0 && y > 0) ? Quadrant I
if (x < 0 && y > 0) ? Quadrant II
if (x < 0 && y < 0) ? Quadrant III
if (x > 0 && y < 0) ? Quadrant IV
if (x == 0 && y != 0) ? On y-axis
if (x != 0 && y == 0) ? On x-axis
if (x == 0 && y == 0) ? At origin

Example

using System;

class Program {
   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) {
      Console.WriteLine($"Point (7, -3): {FindQuadrant(7, -3)}");
      Console.WriteLine($"Point (-6, 4): {FindQuadrant(-6, 4)}");
      Console.WriteLine($"Point (0, 5): {FindQuadrant(0, 5)}");
      Console.WriteLine($"Point (0, 0): {FindQuadrant(0, 0)}");
   }
}

The output of the above code is

Point (7, -3): Quadrant IV
Point (-6, 4): Quadrant II
Point (0, 5): On the y-axis
Point (0, 0): At the origin

Using Ternary Operator

The ternary operator provides a more compact way to implement the same logic. Multiple ternary operators are chained together to evaluate all conditions

Example

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[] xValues = {1, -6, -9, 4, 0, 3, 0};
      int[] yValues = {2, 4, -2, -3, 5, 0, 0};

      for (int i = 0; i < xValues.Length; i++) {
         Console.WriteLine($"Point ({xValues[i]}, {yValues[i]}): {FindQuadrant(xValues[i], yValues[i])}");
      }
   }
}

The output of the above code is

Point (1, 2): Quadrant I
Point (-6, 4): Quadrant II
Point (-9, -2): Quadrant III
Point (4, -3): Quadrant IV
Point (0, 5): On the y-axis
Point (3, 0): On the x-axis
Point (0, 0): At the origin

Comparison

Conclusion

Determining quadrants in C# is straightforward using coordinate sign analysis. Both if-else conditions and ternary operators provide O(1) solutions, with if-else being more readable for complex logic and ternary operators offering more compact code for simple cases.