CONSTRUCTION OF LINE SEGMENT

Construction of line segment :

A line segment is the shortest that connects two given points, but a line has no end points.

The line segment joining the two points A and B can be simple written as AB or the line segment AB.

Length of the line segment AB  =  length of the line segment BA

A line segment can be measured either with a ruler or divider.

Construction of a line segment - Examples

Example 1 :

Draw a line segment AB  =  5.8 cm using a ruler.

Step 1 :

Draw a line "l" and mark a point A on it.

Step 2 :

Fix a ruler on the line. Fix it in such a way that the zero on the scale and the point "A" coincides.

Step 3 :

(i) From A, measure 5.8 cm

(ii) Mark the point as B.

(iii) AB = 5.8 cm is the required segment.

Example 2 :

With the help of a ruler and compass, draw a line segment PQ  =  2.5 cm

Step 1 :

Draw a line "l" and mark a point P on it.

Step 2 :

With the help of a compass, measure 2.5 cm as shown in the figure.

Step 3 :

(i) Place the sharp edge of the compass at P.

(ii) Then with the pencil, draw a small arc on "l" to cut the line. mark the point as "Q".

(iii) PQ = 2.5 cm is the required line segment.

Apart from the stuff "construction of line segment", let us come to know some more stuff about line, ray, line segment and plane.

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.  Draw the straight lines 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. Draw a straight line passing through the points P, Q and R.

Solution :

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

2.  Since A, B and C are 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.

After having gone through the stuff given above, we hope that the students would have understood "Construction of line segment".

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