Page 224 - Ganit Kaushal

Step 2: On a ruler, place the pointer of the compass 5 cm
from the pencil’s lead. (See figure (i))

Step 3: Place the pointer of the compass without disturbing
its opening at point A and mark a small arc on the line l
with the pencil point at B. (See figure (ii)) A B l

Step 4: AB is the required line segment of length 5 cm. (i) (ii)

l
A 5 cm B Remark
Construction 3: Draw a line segment of length A line can be drawn more easily with the help of a
7.3 cm using a ruler only. ruler only as shown in the following construction.
Sol. Follow the steps given below:
A B
Step 1: Mark a point A on a sheet of paper.
Step 2: Place the 0 mark of the ruler at point A.

Step 3: Mark a point B on the sheet at a distance of 7.3 cm from point A.
Step 4: Join points A and B.

Step 5: Then, AB is the required line segment. A 7.3 cm B
 Having learnt about the construction of a circle and a line, let us learn an important application of it.

Perpendicular Bisector of a Line Segment

The perpendicular bisector of a line is a line that is perpendicular to it and bisects it.
Construction 4: Draw the perpendicular bisector of a line segment using a ruler and compass.

Sol. Follow the steps given below:

Step 1: Draw a line segment AB of any length. A B
Step 2: Taking A as the centre, (put the pointer of the compass at A), draw a circle using the compass.
The radius of the circle should be more than half the length of AB. [See figure (i)]

Step 3: Taking point B as the centre and with the same radius, draw another circle using the compass.
Let it cut the previous circle at points C and D. Join CD. Mark the point as O where it cuts the line AB.
Then, CD is the required perpendicular bisector of AB, and O is the midpoint of AB. [See figure (ii)]

C

A B A O B

D
(i) (ii)
CAN YOU THINK?

Are all points that lie on the perpendicular bisector equidistant from A and B?
Yes, they are.

222 Mathematics-6