LINES INTERVALS AND RAYS

Line

What is a line ?

Line is a geometrical object that is straight, endless and thin. It is continuous and we can increase the length, straight or curved. It will not have thickness; the trace of proceeding points.

As the space in between the points decreases they join to form a line. A line is a set of points closely arranged without gap. 

Mark A, B on a sheet of paper using a scale and draw a line passing through these points. 

This is a straight line. 

It is represented as straight line AB or line l. 

When we represent a straight line as AB, it means,

(i)  The line passes through the points A and B.

(ii)  The line extends on either side of A and B. 

Observe the names given for the following straight lines.

Ray

A ray starts from a fixed point and extends indefinitely in other direction.  

1.  Starting point of the ray is A.

2.  The ray passes through the points A and B. 

3.  The ray extends through the point B. 

A ray is a straight line with a starting point and extends indefinitely in one direction. 

Line Segment

If a sheet of paper is folded and then opened, the folded part represents the line segment.

It is shown in the figure given below. 

Mark X, Y and Z on the straight line AB.

Consider AX a part of the straight line, which starts at A and ends at X. So, it has a particular length. This is called a line segment. It can be denoted as line segment AX. 

Few more line segments from the above figure are AY, AB, XY, XB, YB, XZ. 

Therefore line segment is a part of a line. It has a starting point and end point.

A line segment has definite length. 

Intervals

An interval is a connected portion of the real line. If the endpoints  and  are finite and are included, the interval is called closed and is denoted [a, b]. 

If the endpoints are not included, the interval is called open and denoted (a, b). 

If one endpoint is included but not the other, the interval is denoted or and is called a half closed interval (or half-open interval).

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