Question
Draw a line segment of length $6.5\ cm$ and divide it into four equal parts, using ruler and compasses.
✓
Answer
First of all, we construct $AB$ of length $6.5\ cm.$ Now, steps of construction are as follows:
Step I: Draw a line segment $AB = 6.5\ cm.$
Step II: Draw perpendicular bisector of $AB,$ which meets $AB$ at $O (\therefore O$ is the mid point of $AB),$ i.e. $AO = OB.$
Step III: Now, draw perpendicular bisector of $AO$ which meet $AB$ at $P,$ such that $AP = PO.$
Step IV: Then, draw perpendicular bisector of $BO$ which meet $AB$ at $Q,$ such that $BQ = OQ.$
Step V: The line segment $AB$ is divided into $4$ equal parts at $P O$ and $Q.$
Step VI: By actual measurement, we have $AP = PO = OQ = QB = 1.625\ cm.$
Step I: Draw a line segment $AB = 6.5\ cm.$
Step II: Draw perpendicular bisector of $AB,$ which meets $AB$ at $O (\therefore O$ is the mid point of $AB),$ i.e. $AO = OB.$
Step III: Now, draw perpendicular bisector of $AO$ which meet $AB$ at $P,$ such that $AP = PO.$
Step IV: Then, draw perpendicular bisector of $BO$ which meet $AB$ at $Q,$ such that $BQ = OQ.$
Step V: The line segment $AB$ is divided into $4$ equal parts at $P O$ and $Q.$
Step VI: By actual measurement, we have $AP = PO = OQ = QB = 1.625\ cm.$
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