What is a Line Segment, Ray, Point & Line in Math? (Understanding Geometry with Definitions & Examples) - BYJUS

# Concept of Points, Lines and Rays

Points, lines, and rays form the basic building blocks of geometry. All lines and rays start and end with a point. Most shapes are made up of multiple lines. Here we will discuss the significance of a point, the difference between lines, line segments, rays, and various types of lines....Read MoreRead Less

## What is the Point ?

A point is represented as a dot, which denotes a very specific location. It has no dimensions, i.e. no width, length, or depth.

## What is a Line and a Line Segment?

When two points are joined by a straight line you get a line segment, when it is extended indefinitely on both ends which is represented by arrows at both ends, we get a line. It has no beginning and no end in both directions (infinite). A line is one-dimensional.

Line AB

Line segment TS

## What is a Ray?

A ray has two points joined by a straight line segment. But at one point the line extends indefinitely and at the other point it does not. Hence, rays extend only in one direction.

When naming a ray, it is shown by putting a little ray symbol on the top of the two points and the arrow depicts the direction in which the ray extends. For example:

## Types of Lines

1. Intersecting lines
2.Parallel lines
3. Perpendicular lines

(1)  Intersecting lines :

Intersecting lines are formed when any two lines cross each other. The point of intersection is a common point that exists on both intersecting lines. Intersecting lines meet at one point.

Lines AB and CD intersect at point P.

(2) Parallel lines:

Parallel lines are defined as two or more lines that reside in the same plane but never intersect. The corresponding points at these lines are at a constant distance from each other.

The above lines are parallel. They are at a constant distance from each other. They never intersect with each other.

Parallel lines are denoted by the symbol ||.

EF And HG are parallel lines. It is written as EF||GH.

(3) Perpendicular lines:

Perpendicular lines are two intersecting lines that intersect at 90 degrees.

The sign ⟂ is used to symbolise that two lines are perpendicular. The symbol means “is perpendicular to”.

In the given figure AB is perpendicular to CD or AB ⟂ CD.

## Solved Examples on Rays, Lines, Line Segment & Points

Example 1:

1. Name a pair of parallel lines in the figure?
2.Name a pair of perpendicular lines in the figure?
3. Name a pair of intersecting lines?

1. Lines PQ and RS are the pair of parallel lines. They are at the same distance from each other at any point.
2.Line TU is perpendicular to line PQ.
3. Line AB intersects PQ at C and line AB also intersects line RS and line TU at W.

Example 2: A line RQ is parallel to the line PS and another line intersects both lines at A and B points, but the intersecting line is not perpendicular to the other two lines. Draw and label the diagram.

PS and QR are parallel and a line intersects PS at B and RQ at A such that the intersecting line AB is not perpendicular to lines PS and RQ.

Example 3: Observe the figure given below and identify or name:

1. All the points
2.Any two line segments
3. Any Three rays
4. Two different lines

Solution:

a. A point is represented as a dot. Hence, the points in the given figure are A, B, C, D, E and F.

b. The points B, D are joined by a straight line so that you get a line segment $$\overline{\text{BD}}$$

The points B, F are joined by a straight line so that you get a line segment $$\overline{\text{BF}}$$.

c. The two points B, E joined by a straight line segment which is extended at one side forms a ray BE.

The two points B, C joined by a straight line segment which is extended at one side forms a ray BC.

The two points B, A joined by a straight line segment which is extended at one side forms a ray BA.

d. A line AC is extended indefinitely on both ends which are represented by arrows at both ends, hence we get a line.

Example 4: Observe the figure given below and identify or name:

a. A line that contains the point Q.
b.The end point of the ray QT
c. Any two opposite rays

Solution:

a.  A point is represented as a dot. The line that contains the point Q is ST.

b.  The two points Q, T joined by a straight line segment forms a ray QT. From the figure the end point of the ray QT is Q.

c.  The two opposite rays are ray QT and ray QS.

Example 5: There are different roadways between each pair of cities on the map. Can you draw a way using line segments to represent the travel starting from Oswego and back to Oswego through Rochester, Buffalo, Endicott and Syracuse?

Solution:

One way to represent the journey, we draw a:

• Line segment from Oswego to Rochester.
• Line segment from Rochester to Buffalo.
• Line segment from Buffalo to Endicott.
• Line segment from Endicott to Syracuse.
• Line segment from Syracuse to Oswego.

Frequently Asked Questions on Lines & Line Segment

A pair of opposite rays are two rays that extend in opposite directions and have the same endpoint. As a result, a pair of opposite rays always form a line. Hence two rays can form a line.

Perpendicular lines are formed when two lines intersect at 90 degrees. Therefore, all perpendicular lines are intersecting lines. But all intersecting lines are not perpendicular.