Question

Bisect a line of length 7cm. Write down the steps of construction.

Answer 1

Hint: Draw a line AB of length 7cm. With more than half of 7cm draw arcs from one vertex A to each side of AB and repeat this with the vertex B. The arcs draw from vertex B cuts the arcs drawn from vertex A at both sides of AB. Join those intersecting points which makes another line and this line bisects the line AB.


Complete step-by-step Solution:
We are given a line of length 7cm.
Let the line be AB.

With A as centre and radius more than half of 7cm, draw arcs from A to both sides of AB using a compass.

Now repeat the above step with B as centre using a compass, cutting the arcs drawn from A at E and F.

Join the points E and F to make a line EF.

The line EF intersects the line AB let say at M. M is the midpoint of AB which means M bisects AB.

The length of AM will be equal to half of AB.
$
  AM = \frac{1}{2}\left( {AB} \right) \\
  AB = 7cm \\
  AM = \frac{1}{2} \times 7 \\
  AM = 3.5cm \\
$
The length of AM=BM=3.5cm


Note: Bisect means to divide into two equal parts. We can bisect lines, angles, etc. The dividing line is called the bisector. Here the line EF is called the bisector and M is called bisecting point.