Find the Quadrant of Given Coordinates | Program & Explanation

The Cartesian plane is divided into four quadrants based on the signs of the x and y coordinates:

1. Quadrant 1 (First Quadrant) → (x > 0, y > 0)
2. Quadrant 2 (Second Quadrant) → (x < 0, y > 0)
3. Quadrant 3 (Third Quadrant) → (x < 0, y < 0)
4. Quadrant 4 (Fourth Quadrant) → (x > 0, y < 0)

Special Cases:

• Origin (0, 0) → Lies at the center of the coordinate system.
• X-Axis (x ≠ 0, y = 0) → Lies on the x-axis.
• Y-Axis (x = 0, y ≠ 0) → Lies on the y-axis.

Algorithm to Determine the Quadrant

1. Input the values of x and y.
2. Check conditions using if-else statements:
   • If x > 0 and y > 0, it is in Quadrant 1.
   • If x < 0 and y > 0, it is in Quadrant 2.
   • If x < 0 and y < 0, it is in Quadrant 3.
   • If x > 0 and y < 0, it is in Quadrant 4.
   • If x == 0 and y == 0, it is the Origin.
   • If x == 0 and y ≠ 0, it lies on the Y-Axis.
   • If x ≠ 0 and y == 0, it lies on the X-Axis.
3. Print the quadrant or special case based on the condition.

C Program to Find the Quadrant of Given Coordinates

cCopyEdit#include <stdio.h>

int main() {
    int x, y;

    // Input the coordinates
    printf("Enter the x and y coordinates: ");
    scanf("%d %d", &x, &y);

    // Determine the quadrant or special case
    if (x > 0 && y > 0) {
        printf("The point (%d, %d) lies in Quadrant 1.\n", x, y);
    } else if (x < 0 && y > 0) {
        printf("The point (%d, %d) lies in Quadrant 2.\n", x, y);
    } else if (x < 0 && y < 0) {
        printf("The point (%d, %d) lies in Quadrant 3.\n", x, y);
    } else if (x > 0 && y < 0) {
        printf("The point (%d, %d) lies in Quadrant 4.\n", x, y);
    } else if (x == 0 && y == 0) {
        printf("The point (%d, %d) lies at the Origin.\n", x, y);
    } else if (x == 0) {
        printf("The point (%d, %d) lies on the Y-Axis.\n", x, y);
    } else {
        printf("The point (%d, %d) lies on the X-Axis.\n", x, y);
    }

    return 0;
}

Explanation of the Program

1. User enters values for x and y as input.
2. Conditions check which quadrant the point belongs to.
3. Special cases (Origin, X-Axis, Y-Axis) are handled separately.
4. The appropriate output is printed based on the input coordinates.

Test Cases

Complexity Analysis

• The time complexity is O(1) because it involves a constant number of comparisons.
• The space complexity is O(1) as only a few integer variables are used.

Conclusion

• This program effectively determines the quadrant in which a point lies.
• Handles special cases such as the Origin, X-Axis, and Y-Axis.
• Uses if-else conditions to make comparisons efficiently.
• Works for both positive and negative values of x and y.

This type of program is frequently asked in placement exams as