Collinear
Pronunciation: /koʊˈlɪn.i.ər/ Explain
Click on the points and drag them to change the figure.
 Manipulative 1  Collinear Points Created with GeoGebra. 

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).


Figure 1: Collinear points


Figure 2: Noncollinear points


Related Words
Collinearity: Having to do with whether
or not objects are in the same line.
How to tell if Points are Collinear

Figure 3: Graph with 3 points.


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. 
References
 McAdams, David E.. All Math Words Dictionary, collinear. 2nd Classroom edition 201501084799968. pg 36. Life is a Story Problem LLC. January 8, 2015. Buy the book
 Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid. pg 5. Translated by Casey, John, LL.D. F.R.S.. www.archive.org. Hodges, Figgis & Co.. 1890. Last Accessed 6/25/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/5/mode/1up/search/collinear. Buy the book
 Palmer, Claude Erwin and Taylor, Daniel Pomeroy. Solid Geometry. pg 280. www.archive.org. Scott, Foresman and Company. 1918. Last Accessed 6/25/2018. http://www.archive.org/stream/solidgeometry00palmrich#page/280/mode/1up/search/collinear. Buy the book
Cite this article as:
McAdams, David E. Collinear. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/collinear.html.
Image Credits
Revision History
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (
McAdams, David E.)
3/15/2010: Improved instructions for manipulative 3. Added section on analytical geometry. (
McAdams, David E.)
1/12/2010: Added "References". (
McAdams, David E.)
7/5/2008: Added More Information. (
McAdams, David E.)
8/23/2007: Initial version. (
McAdams, David E.)