# C++ Program to Check if a Given Set of Three Points Lie on a Single Line or Not

This is a C++ program to check if a given set of three points lie on a single line or not. Three points lie on a single line if the area of the triangle formed by this points is equal to zero.

The area of the triangle is −

0.5 * (x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)).

## Algorithms

Begin
Generate the points randomly.
Calculate the area by using above formula.
If area > 0
Then the points don't lie on the straight line.
else if area < 0
Then the points don't lie on the straight line.
else
The points lie on the straight line.
End

## Example

#include <iostream>
#include <time.h>
#include <stdlib.h>
using namespace std;
static int L = 1;
static int U= 20;
int main(int argc, char **argv) {
int x3, y3, x1, x2, y1, y2;
time_t seconds;
time(&seconds);
srand((unsigned int) seconds);
//Generate the points randomly using rand().
x1 = rand() % ( U- L+ 1) + L;
y1 = rand() % (U - L+ 1) + L;
x2 = rand() % (U - L + 1) + L;
y2 = rand() % (U - L+ 1) + L;
x3 = rand() % (U - L+ 1) + L;
y3 = rand() % (U - L+ 1) + L;
cout << "The points are: (" << x1 << ", " << y1 << "), (" << x2 << ", " << y2 << "), & (" << x3 << ", " << y3 << ")\n";
//calculate area
float a = 0.5 *(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2));
if (a < 0)
cout << "The points don't lie on the straight line";
else if (a > 0)
cout << "The points don't lie on the straight line ";
else
cout << "The points lie on the straight line";
}

## Output

The points are: (20, 9), (6, 13), & (13, 11)
The points lie on the straight line

The points are: (9, 15), (4, 15), & (11, 16)
The points don't lie on the straight line