Page 36 - Ganit Kaushal

Practically, we can make a line segment by joining two given points as follows:

Take a piece of paper. Mark two points A and B on the edges of the paper as shown in the figure below. Now
fold the piece of paper through the given points A and B and press the two parts together. On unfolding the
two parts, we find that a straight crease is formed passing through points A and B. This straight crease in the
paper is an example of a line segment joining the points A and B.

A A
Crease Part of line

B B
Piece of paper Unfolding the paper

Folding the paper
The length of the line segment AB is denoted by AB (without a bar). Two line segments, AB and CD, are said
to be equal if and only if they are of equal length. This is written as:
AB = CD if and only if AB = CD
Line

If a line segment joining two points A and B is extended along both directions (beyond the A B
points A and B indefinitely, i.e., without end points), it is known as a line. A line through

two points A and B is denoted as AB. It extends forever in both directions. Sometimes a
line is denoted by a letter such as l or m as shown in the adjacent figure.
• Any two points determine a unique line that passes through both of them. A
• Through one given point A, there pass infinitely many lines (see adjoining
figure).

Collinear Points

Three or more points that lie on the same line are called collinear points. Points A, B and
C in the adjacent figure are collinear points. A B C

Ray

A ray is a portion of a line. It has one end point, called the starting point or the initial point of the ray, and
extends indefinitely in another direction, as shown in the figure alongside. ‘Ray AB’ is

denoted by putting an arrow over it. So, AB is read as ‘ray AB’. A ray is completely A Ray AB B
defined by its initial point and its direction.

A ray has a particular direction, so, unlike line segments, AB and BA don’t represent the same ray. They

are in opposite directions and have different initial points. The initial point of AB is A while the initial point

of BA is B. So, AB and BA are not the same ray.
A B
Unlike a line segment, a ray has no measurable length as it extends indefinitely in a direction. Ray BA
Two rays with the same initial point but extending in opposite directions are called opposite rays.
Draw a line l and mark a point O on it. Then mark two points, say A and B, on opposite sides of O on this line.

We get two rays OA and OB with the same initial point O, and extending indefinitely in opposite directions.

OA and OB are the opposite rays (see adjoining figure). A O B l
34 Mathematics-6