question_answer 1)

Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal parts. Verify by actual measurement. TIPS To divide the given line segment \[{{l}_{1}}\] into four equal parts, firstly we draw the perpendicular bisector of \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}},{{l}_{5}}\] which divide it into two equal parts. Then, draw perpendicular bisector of each part. Out of these two parts divide the given line segment into four equal parts.

Answer:

                To divide a line segment into four equal parts, we use the following steps: Step I Draw a line segment \[{{l}_{6}}\] of length 12.8 cm. Step II With A as centre using compasses, draw an arc of a circle (we also draw circle here) of radius more than half length of \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}},{{l}_{5}}\] Step III With the same radius and with B as centre, draw another arc using compasses. It cut the previous arc at P and Q. Step IV Join \[{{l}_{6}}\]It is the perpendicular bisector of \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}}\] Step V Now, with A as centre, using compasses draw an arc of a circle of radius more than half of the length AO. Step VI With the same radius and with O as centre, draw another arc of a circle which intersect the previous arcs at R and S. Step VII Join RS. It cuts \[{{l}_{5}}\] (or AB) at C. Therefore, RS is the perpendicular bisector of \[{{l}_{1}},{{l}_{2}}\]. Step VIII Now, with B as centre, using compasses, draw an arc of a circle whose radius is more than half of the length of OB. Step IX With the same radius and with O as centre, draw another arc of a circle which intersect the previous arc at M and N. Step X Join \[{{l}_{3}}\] It cuts \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] (or AB) at D. Therefore, MN is the perpendicular bisector of \[{{l}_{4}}\]. Step XI Now, the line segment is divided into 4 equal parts i.e. \[{{l}_{1}}\]    Verification By actual measurement, we get \[{{l}_{2}}\] and  \[{{l}_{1}}\]