C Exercises: Check if a point (x, y) is within a triangle or not

Last update on September 19 2025 12:44:53 (UTC/GMT +8 hours)

Check if a point lies within a triangle

Write a C program to check if a point (x, y) is within a triangle or not. Three points make up a triangle.

Input:
x1,y1,x2,y2,x3,y3,xp,yp separated by a single space

Sample Solution:

C Code:

#include <stdio.h>

// Function to calculate the outer product of two vectors
double check_outer_product(double X1, double Y1, double X2, double Y2) {
  return X1 * Y2 - X2 * Y2;
}

int main() {
  double x[3], y[3], xp, yp, cop1, cop2, cop3;

  // Prompting the user to input three points to form a triangle
  printf("Input three points to form a triangle:\n");
  scanf("%lf %lf %lf %lf %lf %lf", &x[0], &y[0], &x[1], &y[1], &x[2], &y[2]);

  // Prompting the user to input a point to check if it's inside the triangle
  printf("\nInput the point to check if it is inside the triangle or not:\n");
  scanf("%lf %lf", &xp, &yp);

  // Calculating the outer products using the function
  cop1 = check_outer_product(x[1] - x[0], y[1] - y[0], xp - x[0], yp - y[0]);
  cop2 = check_outer_product(x[2] - x[1], y[2] - y[1], xp - x[1], yp - y[1]);
  cop3 = check_outer_product(x[0] - x[2], y[0] - y[2], xp - x[2], yp - y[2]);

  // Checking if the point is inside or outside the triangle based on outer products
  if (((cop1 > 0.0) && (cop2 > 0.0) && (cop3 > 0.0)) ||
      ((cop1 < 0.0) && (cop2 < 0.0) && (cop3 < 0.0))) {
    printf("The point is inside the triangle!");
  } else {
    printf("The point is outside the triangle!");
  }

  return 0; // End of the program
}

Sample Output:

Input three points to form a triangle:
x1 y1 z1

Input the point to check it is inside the triangle or not:
The point is outside the triangle!

Flowchart:

C Programming Flowchart: Check if a point (x, y) is within a triangle or not.

For more Practice: Solve these Related Problems:

Write a C program to determine if a point is inside a triangle using the area method.
Write a C program to check point inclusion in a triangle by comparing barycentric coordinates.
Write a C program to use cross-product calculations to verify if a point lies within the bounds of a triangle.
Write a C program to implement a function that calculates areas and determines if a point is inside a triangle.

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