Program to check if three points are collinear

Given three points, check whether they lie on a straight (collinear) or not
Examples : 
 

Input : (1, 1), (1, 4), (1, 5)
Output : Yes 
The points lie on a straight line

Input : (1, 5), (2, 5), (4, 6)
Output : No 
The points do not lie on a straight line

 

First approach 
Three points lie on the straight line if the area formed by the triangle of these three points is zero. So we will check if the area formed by the triangle is zero or not
 

Formula for area of triangle is : 
0.5 * [x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)]

The formula is basically half of determinant
value of following.
x1 x2 x3
y1 y2 y3
1 1 1

The above formula is derived from shoelace formula.

If this equals zero then points lie on a straight line 

Output : 
 

Yes

Time Complexity: O(1)

Auxiliary Space: O(1)
 
Second approach 
 

For three points, slope of any pair of points
must be same as other pair.

For example, slope of line joining (x2, y2)
and (x3, y3), and line joining (x1, y1) and
(x2, y2) must be same.

(y3 - y2)/(x3 - x2) = (y2 - y1)/(x2 - x1)

In other words, 
(y3 - y2)(x2 - x1) = (y2 - y1)(x3 - x2) 

 

Output : 
 

No 

Time Complexity: O(1)

Auxiliary Space: O(1)