Collinear
Pronunciation: /koʊˈlɪn.i.ər/ Explain
Click on the points and drag them to change the figure.
| Manipulative 1 - Collinear Points Created with GeoGebra. |
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If points are collinear, they are in the same
line[2][3].
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 non-collinear, no one line can be drawn
that contains all the objects (see figure 3).
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Figure 1: Collinear points
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Figure 2: Non-collinear points
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Related Words
Collinearity: Having to do with whether
or not objects are in the same line.
How to tell if Points are Collinear
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Figure 3: Graph with 3 points.
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In 2-dimensional
analytical geometry,
each point has an
x-coordinate
and a
y-coordinate.
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.
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Step | Equation(s) | Discussion |
1 |
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This
algorithm
starts with the equation of a line in point slope form. |
2 |
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Start by selecting any two of the points. For this demonstration,
select (-1,-1) and
(3,1). |
3 |
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Use the slope formula to determine the slope of the line defined by the two points. |
4 |
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Now pick one of the points already used and the third point. |
5 |
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Find the slope of the line defined by those two points. |
6 |
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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 20150108-4799968. 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. 4/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://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.)