Question

Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal parts. Verify by actual measurement

Answer 1

A perpendicular bisector of a line segment is a line segment perpendicular to and passing through the midpoint of the line segment.

Steps of construction:

(i) Draw a line segment AB = 12.8 cm
(ii) Draw the perpendicular bisector of $\overline{AB}$ which cuts it at C. Thus, C is the midpoint of $\overline{AB}$.
(iii) Draw the perpendicular bisector of $\overline{AC}$ which cuts it at D. Thus D is the midpoint of.
(iv) Again, draw the perpendicular bisector of $\overline{CB}$ which cuts it at E. Thus, E is the mid-point of CB.
(v) Now, point C, D and E divide the line segment $\overline{AB}$ in the four equal parts.
(vi) By actual measurement, we find that $\overline{AD}=\overline{DC}=\overline{CE}=\overline{EB}=3.2cm$