
If points are collinear, they are in the same line^{1}. Since two points define a line, any two points are collinear (see figure 1). If three points are collinear, a line drawn using any two of the points will contain the third (see figure 2). If objects are noncollinear, no one line can be drawn that contains all the objects (see figure 3). 

Collinearity: Having to do with whether or not objects are in the same line.

In 2dimensional analytical geometry, each point has an xcoordinate and a ycoordinate. These coordinates can be used to see if three are collinear. To see if three or more points are collinear, pick one of the points as a reference point. If the slopes of the lines defined by the reference point and each of the other points are equal, the points are collinear. Table 1 shows the steps for determining if the points in figure 3 are collinear. 
Step  Equation(s)  Discussion 

1  This algorithm starts with the equation of a line in point slope form.  
2  Start by selecting any two of the points. For this demonstration, select (1,1) and (3,1).  
3  Use the slope formula to determine the slope of the line defined by the two points.  
4  Now pick one of the points already used and the third point.  
5  Find the slope of the line defined by those two points.  
6  Since the slopes are equal, the three points are collinear.  
Table 1: How to find out if three points are collinear. 
#  A  B  C  D 
E  F  G  H  I 
J  K  L  M  N 
O  P  Q  R  S 
T  U  V  W  X 
Y  Z 
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