Lesson Introduction to line, ray and segments

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In this lesson we will develop basic understanding of Points,Lines,Rays and Segment and look into their basic properties.

Point

{{{drawing( 160, 160, -6, 6, -6, 6, circle( 0, 0, 0.2 ), circle(-4,4,0.2),circle( 5, 5, 0.2 ), circle( 5.4, -6.9, 0.2 ), circle( 2, 2, 0.2 ), circle( -4.5,-6.5, 0.2 ), circle( -5.5, -4.1, 0.2 ), circle( 0, 0, 0.2 ))}}}

A spatial point or in a point is a concept used to define an exact location in space. They pinpoint a location in space and gives it unique <A HREF=Coordinates_(elementary_mathematics).wikipedia>coordinates</A>.

All the dots shown in figure are points in space.

It has following features:

1> It has no volume, area or length.

2> In mathematics generally or any form of space is considered to be made up of points as basic elements.

3>A group of points joined together define any figure in space.

{{{drawing( 160, 160, -6, 6, -6, 6,grid( 1 ),line( -4.6, -3.5, -6, 6 ),line( -2,-6, 7, -0.5 ), line(4, 4,-5.1, -4 ))}}}

A line is a set of infinite points joined together in a plane to form a infinitively small straight curve. This curve extends both sides to infinity.

Following are some features of a line:

1>In <A HREF=http://www.algebra.com/algebra/about/history/Euclidean-Geometry.wikipedia>Euclidean geometry</A>, exactly one line can be found that passes through any two points.

2>The line provides the shortest distance between any two points in a space.

3> Two different lines in a plane must either be parallel lines or must intersect at one point.

2>Two lines if not lying on same plane may neither intersect or be parallel to each other, such lines are called <A HREF=Skew_line.wikipedia>skew lines</A>.

3>In a Three Dimensional space two planes will intersect at a group of points to form a line.

4>If three or more points lie on the same line are called <A HREF=http://dictionary.algebra.com/words/Collinear_points.xlwikipedia>collinear</A>.

5> The <A HREF=http://www.algebra.com/algebra/homework/Linear-equations/Polynomial-Expressions-and-Equations-in-Color.lesson>equation of a line</A> is {{{y=mx+c}}}
where x and y are intercepts on x and y axis respectively.
m is slope of line and c is a constant.

{{{drawing( 160, 160, -6, 6, -6, 6, line( -5,0,5,0),circle(-5,0,.3),circle(-1,0,.3),circle(2,0,.3),locate(-5,1.5,A),locate(-1,1.5,B),locate(2,1.5,C),line(5,0,4,0.5),line(5,0,4,-0.5))}}}

A straight line, limited from one side and infinite from another side, is called a ray. It is shown in the figure.

In geometry, a ray starts at one point, then goes on forever in one direction. A ray has a originating point and it extends in a direction. It is different from a line as it is allowed to extend only in one particular direction unlike line.

No point in a ray can lie on left side of A as shown in diagram, as it is the originating point.

The ray will have same <A HREF=http://www.algebra.com/algebra/homework/Graphs/slope.wikipedia>slope</A> as of a line.

Segment

{{{drawing( 160, 160, -6, 6, -6, 6, line( -3,0,3,0),circle(-3,0,.3),circle(3,0,.3),locate(-3,1.5,A),locate(3,1.5,B))}}}

In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. It is as shown in the figure.

Examples of line segments include the sides of a <A HREF=Triangle.wikipedia>triangle</A> or <A HREF=Triangle.wikipedia>square</A>.

The Segment will have same slope as of line.