POINT LINE LINE SEGMENT RAY AND PLANE

Point

Point is not something new to us. Many graphs are being drawn using points.

A point is smaller than a tip of a pencil or pen used by us. Therefore a point has not length, width, height or thickness. 

A point indicates a definite position. 

Points are usually denoted by capital letters A, B, C and so on as given below. 

Line

Observe the figure given below carefully. 

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. 

Plane

Straight lines, points and rays can be represented in a sheet of paper or on the black board. Isn't it ?

Likewise floor, wall, black board, card board and top portion of the table are few examples of plane. 

A plane is a flat surface which extends indefinitely in all directions as given in the figure given below. 

How many points are required to form a plane ? 

It is enough to have three points that do not lie on the same straight line. 

Relation between Points and Lines

Collinear Points :

1.  Check whether you can draw a straight line passing through the points A and B.

2. Check whether you can draw a straight line passing through the points A, B and C.

3.  Check whether you can draw a straight line passing through the points P, Q and C.

Answers :

1. You can draw a straight line passing through the two points A and B. 

2.  Since A, B and C are not on the same straight line, a straight line can not be drawn through A, B and C. 

3.  A straight line can be drawn through P, Q and R, as they lie on the same straight line. 

So, P, Q and R are collinear points. 

Hence, the following statements are true. 

(i)  A straight line can be drawn through any two given points.

(ii)  It is not always possible to draw a straight line passing through any 3 points. 

(iii) But a straight line can be drawn passing through 3 collinear points. 

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