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We're looking forward to your contributions.\n\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></div><div class=mw-indicators></div><h1 class=firstHeading id=firstHeading>Geometry/Points, Lines, Line Segments and Rays</h1><div class=vector-body id=bodyContent><div class=noprint id=siteSub>From Wikibooks, open books for an open world</div><div id=contentSub><span class=subpages> < <a href=/wiki/Geometry title=Geometry> Geometry </a> </span></div><div id=contentSub2></div><div id=jump-to-nav></div><a class=mw-jump-link href=#mw-head> Jump to navigation </a><a class=mw-jump-link href=#searchInput> Jump to search </a><div class="mw-body-content mw-content-ltr"dir=ltr id=mw-content-text lang=en><div class=mw-parser-output><p>Points and lines are two of the most fundamental concepts in Geometry, but they are also the most difficult to define. We can describe intuitively their characteristics, but there is no set definition for them: they, along with the plane, are the undefined terms of geometry. All other geometric definitions and concepts are built on the undefined ideas of the point, line and plane. Nevertheless, we shall try to define them.<div aria-labelledby=mw-toc-heading class=toc id=toc role=navigation><input class=toctogglecheckbox id=toctogglecheckbox role=button style=display:none type=checkbox><div class=toctitle dir=ltr lang=en><h2 id=mw-toc-heading>Contents</h2><span class=toctogglespan> <label class=toctogglelabel for=toctogglecheckbox></label> </span></div><ul><li class="toclevel-1 tocsection-1"><a href=#Point> <span class=tocnumber> 1 </span> <span class=toctext> Point </span> </a><li class="toclevel-1 tocsection-2"><a href=#Line> <span class=tocnumber> 2 </span> <span class=toctext> Line </span> </a><li class="toclevel-1 tocsection-3"><a href=#Ray> <span class=tocnumber> 3 </span> <span class=toctext> Ray </span> </a><li class="toclevel-1 tocsection-4"><a href=#Plane> <span class=tocnumber> 4 </span> <span class=toctext> Plane </span> </a><li class="toclevel-1 tocsection-5"><a href=#Space> <span class=tocnumber> 5 </span> <span class=toctext> Space </span> </a><li class="toclevel-1 tocsection-6"><a href=#N-dimensional_Space> <span class=tocnumber> 6 </span> <span class=toctext> N-dimensional Space </span> </a><li class="toclevel-1 tocsection-7"><a href=#Further_reading> <span class=tocnumber> 7 </span> <span class=toctext> Further reading </span> </a></ul></div><h2><span class=mw-headline id=Point> Point </span> <span class=mw-editsection> <span class=mw-editsection-bracket> [ </span> <a title="Edit section: Point"class=mw-editsection-visualeditor href=/w/index.php?title=Geometry/Points,_Lines,_Line_Segments_and_Rays&veaction=edit&section=1> edit </a> <span class=mw-editsection-divider> | </span> <a title="Edit section: Point"href=/w/index.php?title=Geometry/Points,_Lines,_Line_Segments_and_Rays&action=edit&section=1> edit source </a> <span class=mw-editsection-bracket> ] </span> </span></h2><p>A point is an exact location in space. A point is denoted by a dot. A point has no size.<h2><span class=mw-headline id=Line> Line </span> <span class=mw-editsection> <span class=mw-editsection-bracket> [ </span> <a title="Edit section: Line"class=mw-editsection-visualeditor href=/w/index.php?title=Geometry/Points,_Lines,_Line_Segments_and_Rays&veaction=edit&section=2> edit </a> <span class=mw-editsection-divider> | </span> <a title="Edit section: Line"href=/w/index.php?title=Geometry/Points,_Lines,_Line_Segments_and_Rays&action=edit&section=2> edit source </a> <span class=mw-editsection-bracket> ] </span> </span></h2><p>As for a line segment, we specify a line with two endpoints. Starting with the corresponding line segment, we find other line segments that share at least two points with the original line segment. In this way we extend the original line segment indefinitely. The set of all possible line segments findable in this way constitutes a line. A line extends indefinitely in a single dimension. Its length, having no limit, is infinite. Like the line segments that constitute it, it has no width or height. You may specify a line by specifying any two points within the line. For any two points, only one line passes through both points. On the other hand, an unlimited number of lines pass through any single point.<h2><span class=mw-headline id=Ray> Ray </span> <span class=mw-editsection> <span class=mw-editsection-bracket> [ </span> <a title="Edit section: Ray"class=mw-editsection-visualeditor href=/w/index.php?title=Geometry/Points,_Lines,_Line_Segments_and_Rays&veaction=edit&section=3> edit </a> <span class=mw-editsection-divider> | </span> <a title="Edit section: Ray"href=/w/index.php?title=Geometry/Points,_Lines,_Line_Segments_and_Rays&action=edit&section=3> edit source </a> <span class=mw-editsection-bracket> ] </span> </span></h2><p>We construct a ray similarly to the way we constructed a line, but we extend the line segment beyond only one of the original two points. A ray extends indefinitely in one direction, but ends at a single point in the other direction. That point is called the end-point of the ray. Note that a line segment has two end-points, a ray one, and a line none. An angle can be formed when two rays meet at a common point. The rays are the sides of the angle. The point of the end of two rays is called the vertex.<h2><span class=mw-headline id=Plane> Plane </span> <span class=mw-editsection> <span class=mw-editsection-bracket> [ </span> <a title="Edit section: Plane"class=mw-editsection-visualeditor href=/w/index.php?title=Geometry/Points,_Lines,_Line_Segments_and_Rays&veaction=edit&section=4> edit </a> <span class=mw-editsection-divider> | </span> <a title="Edit section: Plane"href=/w/index.php?title=Geometry/Points,_Lines,_Line_Segments_and_Rays&action=edit&section=4> edit source </a> <span class=mw-editsection-bracket> ] </span> </span></h2><p>A point exists in zero dimensions. A line exists in one dimension, and we specify a line with two points. A plane exists in two dimensions. We specify a plane with three points. Any two of the points specify a line. All possible lines that pass through the third point and <b> any </b> point in the line make up a plane. In more obvious language, a plane is a flat surface that extends indefinitely in its two dimensions, length and width. A plane has no height.<h2><span class=mw-headline id=Space> Space </span> <span class=mw-editsection> <span class=mw-editsection-bracket> [ </span> <a title="Edit section: Space"class=mw-editsection-visualeditor href=/w/index.php?title=Geometry/Points,_Lines,_Line_Segments_and_Rays&veaction=edit&section=5> edit </a> <span class=mw-editsection-divider> | </span> <a title="Edit section: Space"href=/w/index.php?title=Geometry/Points,_Lines,_Line_Segments_and_Rays&action=edit&section=5> edit source </a> <span class=mw-editsection-bracket> ] </span> </span></h2><p>Space exists in three dimensions. Space is made up of all possible planes, lines, and points. It extends indefinitely in all directions.<h2><span class=mw-headline id=N-dimensional_Space> N-dimensional Space </span> <span class=mw-editsection> <span class=mw-editsection-bracket> [ </span> <a title="Edit section: N-dimensional Space"class=mw-editsection-visualeditor href=/w/index.php?title=Geometry/Points,_Lines,_Line_Segments_and_Rays&veaction=edit&section=6> edit </a> <span class=mw-editsection-divider> | </span> <a title="Edit section: N-dimensional Space"href=/w/index.php?title=Geometry/Points,_Lines,_Line_Segments_and_Rays&action=edit&section=6> edit source </a> <span class=mw-editsection-bracket> ] </span> </span></h2><p>Mathematics can extend space beyond the three dimensions of length, width, and height. We then refer to "normal" space as 3-dimensional space. A 4-dimensional space consists of an infinite number of 3-dimensional spaces. Etc.<h2><span class=mw-headline id=Further_reading> Further reading </span> <span class=mw-editsection> <span class=mw-editsection-bracket> [ </span> <a title="Edit section: Further reading"class=mw-editsection-visualeditor href=/w/index.php?title=Geometry/Points,_Lines,_Line_Segments_and_Rays&veaction=edit&section=7> edit </a> <span class=mw-editsection-divider> | </span> <a title="Edit section: Further reading"href=/w/index.php?title=Geometry/Points,_Lines,_Line_Segments_and_Rays&action=edit&section=7> edit source </a> <span class=mw-editsection-bracket> ] </span> </span></h2><ul><li><a title="w:Point (geometry)"class=extiw href=https://en.wikipedia.org/wiki/Point_(geometry)> Point </a></ul></div><noscript><img style="border: none; position: absolute;"alt height=1 src=//en.wikibooks.org/wiki/Special:CentralAutoLogin/start?type=1x1 width=1></noscript><div class=printfooter>Retrieved from " <a dir=ltr 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