3rd Class Mathematics Points, Lines and Rays Point, Line and Ray

         Point

 

A figure does not have length, breadth and height but it has position is called point. A figure made by pressing the sharpened end of a pencil on a plane figure is known as point. A letter which denotes a point is the name of the point. The name of the following points are given below:

. P     . M    . L

 

Remember the following about a point:

• A point does not have length, width and height.
• A point has position.
• A point is usually denoted by capital letter of English alphabet.

 

Distance between two points is 5 cm. If a dot is exactly between the two pointsthen find the distance among the middle and each point,                     

A. B. C.    

(a) 2cm

(b) 2.5cm

(c) 3cm

(d) All of these

(e) None of these

 

Answer (b)

Explanation

Middle point is exactly between two points. Hence, distance from both the points to middle point is 2.5 cm.

 

         Line

Innumerous points on a plane in a particular direction form a figure is called a line.

A line has no breadth and thickness. A tight wire between its two ends, edges of a table, edges of a ruler are the examples of lines. A line may be a straight line or curved line.

 

In the above figure straight line I, and another figure curved line p are given. A line is usually denoted by small letters. Therefore, the name of the above lines are   and p. The arrow marks on its both ends indicates that it can be extended from both directions to any length. Line I is represented by   

Remember the following about a line:

• A line does not have fixed length.
• A line can be extended on both directions.
• A line is usually denoted by small letter of English alphabet.

 

 

 

Which one of the following represents a line?

(a)

(b) .............................   

(c)  

(d) All of these  

(e) None of these    

 

Answer (c)  

Expiration:
A line can be extended on both directions.      

 

             Straight Line

A straight line on the horizontal is the shortest distance between two points.

In the figure above, line m is drawn through two points, A and B or two points A and B are shown on the line m, therefore, AB are the points on the line m. Another line can also be drawn between points, A and B but it cannot be a straight line.

Remember the following about a straight line:

• A straight line does not have a fixed length.
• A straight is the shortest distance between two points.
• Only straight line is possible between two points.

 

From the figure given below, find the shortest distance between the points A and B?

 

(a) A curved line AOB

(b) A straight line C

(c) A straight line AB

(d) All of these    

(e) None of these                                                         

 

Answer (c)

Explanations     

A straight line AB is the shortest distance between the points A and B.

 

                Curved Line The line other than straight line between two points is called curved line. Two points can be joined in many ways, therefore, infinitive curved lines are possible between two points. The shortest distance between two points is always a straight line.

In the above figure, AB is the straight line between points A and B therefore, the line AB is the shortest distance between the points.

 

Remember the following about the curved line:

• The line other than straight line between two points is called curved line.
• Length of curved lines which can be drawn between two points is always greater than the length of straight line between the points.
• Infinite curved lines are possible between two given points. 

 

 

In the figure below, two points A and B are joined by curved lines and straight line. Which one of the following options represents the shortest distance between the points?

 

 

(a)   

(b)  

(c)   (d) All of these   (e) None of these     Answer (b)      

 

               

• Line Segment

A line which has definite length is called line segment.

In the figure given below, two end points A and B are taken on the line I, therefore, I is the line and length of AB is the line segment. The arrow marks on both sides of the line show that it goes to any length on each side. Line segment AB is denoted by

 

Remember the following about the line segment:

• A line segment has a fixed length.
• It can't be extended.
• It has two end points.

 

          Comparison between Line and Line Segment

Line	Line segment
1. A line does not have fixed length	1. A line segment has a fixed length.
2. It can be extended on both directions	2. It cannot be extended.
3. It does not have end point.	3. It has two end points.

 

 

 

Identify the lines from the options given below.

(a)  

(b)  

(c)   

(d) All of these   (e) None of these    

 

Answer (d)                                                                      

Explanation AB, PQ and m are lines.                                                     

 

           Ray A ray is a straight line. It has a starting point and it can be extended on the direction     of arrow. In the figure OA is a ray. The ray OA begins from 0 but can go to any     distance on the direction of A. The ray OA is denoted by 

       

In the figure, a ray XY with starting point X can be extended indefinitely on the direction of Y. A ray AB has an initial point B and can be extended indefinitely on the direction of A.   Remember the following about a ray: v  A ray does not have a fixed length. v  It can be extended to any length on a side in a fixed direction. v  It has one end point.  

 

           Comparison between Line and Ray  

LINE	RAY
1. A line has infinitive length.	1. A ray also has infinite length.
2. A line can be extended on both directions	2. A ray can be extended on one direction.
3. It does not have origin.	3.It has origin.
4. Symbol of a line is	4.Symbol of a ray is

 

 

   

Consider the following statements:

Statement 1: A line has a fixed length, it cannot be extended.

Statement 2: A ray does not have fixed length, it can be extended on a direction.

Which one of the following options is correct about the above statements?

(a) Statement 1 is true and 2 is false

(b) Statement 1 is false and 2 is true

(c) Both statements are true

(d) All of these

(e) None of these

 

Answer (b)

Explanation

A ray can be extended in one direction, it does not have fixed length.

 

              Intersecting Point of Lines

A line segment is drawn horizontally from a point 0 to A and another vertical line segment is drawn from 0 to B, thus the origin of both the line segments is same.

Therefore, the common point for both the lines is called its intersecting or meeting point.

In the figure given below, AC and AB meet at A.

CD and AB meet at the point P. and line segment AB and CB meet at the point B.

 

Symbol for the notation of an angle is A letter Q between two line segments also represents the angle. Therefore, the name of the given angle is   ABC or Q. The unit for the measurement of an angle is degree ( ). An angle is measured at a common point between two lines.                

 

In the figure below, two angles  and  have a common arm CE. The vertex C is the common vertex of both the angles. Hence,   DCE is called the adjacent   ECF and denoted by                

 

Remember the following about an angle:

• When two arms or sides meet at a point they include an angle.
• The meeting point of two arms or sides is called the vertex of the angle.
• If two angles have a common arm and common vertex then the angles are called adjacent angles.

 

 

How many vertices are there in the given figure?

(a) 4

(b) 3

(c) 2

(d) None of these

(e) All of these

 

Answer (a)

Explanations

There are four vertices in the given figure.

Therefore, option (a) is correct and rest of the options is incorrect.