Question

Draw a line segment $$AB = 5.6$$ cm and draw its perpendicular bisector. Measure the length of each part.

Answer 1

Hint: Here in this question belongs to construction topic, we have to construct the perpendicular line at point P on the line AB of length 5.6 cm, then construct a perpendicular bisector which bisect a line segment AB by using a geometrical instruments like centi-meter scale, compass with provision of fitting a pencil and protractor.

Complete step-by-step solution:
Perpendicular bisector can be defined as a line segment which intersects or bisect another line perpendicularly or at right angles ($${90^ \circ }$$) and divides it into two equal parts.
Now, consider the given question
Draw a line segment $$AB = 5.6$$ cm and need to draw a perpendicular bisector of line segment AB.
To construct the perpendicular line follow the below steps:
Steps of Construction:
1. Draw a line segment $$AB = 5.6$$ cm

2. Consider point ‘A as centre and take radius more than half of line segment AB, then draw two arcs on each side of the line segment AB.

3. Consider point ‘B’ as centre and take radius more than half of line segment AB (Same radius taken in step 2), then draw two arcs on each side of the line segment AB.

4. Name the point of arc intersection as X and Y.
5. Join the points XY such that it intersects or bisects the line segment AB at the point O. 
6. Measure the length of AO and BO

i.e., $$AO = 2.8$$ cm and $$BO = 2.8$$ cm.

The construction of perpendicular bisector is:

$$\therefore $$ $$XY$$ is the perpendicular bisector of the line segment $$AB$$.

Note: When doing construction handling the instruments carefully, remember when making an arc the radius will be the same which cannot be alter and perpendicular bisector is a line that makes an angle of $${90^ \circ }$$ with another line. $${90^ \circ }$$ is also called a right angle and the line cuts the other line as two equal halves.