Make a line segment of 11 cm and divide it into two equal parts use ruler and compass only

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Draw a line segment of length 6.5cm and divide it into four equal parts, using ruler and compass.

Solution

Steps of construction:

Step I: Draw a line segment $\overline{AB}=6.5cm$

Step II: Draw a perpendicular bisector of AB, which meets $\overline{AB}$ at O

[$\because$ O is the mid-point of $\overline{AB}$, i.e. AO = OB].

Step III: Now, draw a perpendicular bisector of $\overline{AO}$ which meet $\overline{AB}$ at P, such that AP = PO.

Step IV: Then, draw a perpendicular bisector of $\overline{BO}$ which meet $\overline{AB}$ at Q, such that BQ = OQ.

Step V: The line segment $\overline{AB}$ is divided into 4 equal parts at P, O, and Q

Step VI: By actual measurement, we find that $\overline{AP}=\overline{PO}=\overline{OQ}=\overline{QB}=1.625cm.$

Mathematics

NCERT Exemplar

Standard VI