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Question 76

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 ¯¯¯¯¯¯¯¯AB=6.5cm

Step II: Draw a perpendicular bisector of AB, which meets ¯¯¯¯¯¯¯¯AB at O

[ O is the mid-point of ¯¯¯¯¯¯¯¯AB, i.e. AO = OB].

Step III: Now, draw a perpendicular bisector of ¯¯¯¯¯¯¯¯AO which meet ¯¯¯¯¯¯¯¯AB at P, such that AP = PO.

Step IV: Then, draw a 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 find that ¯¯¯¯¯¯¯¯AP=¯¯¯¯¯¯¯¯PO=¯¯¯¯¯¯¯¯¯OQ=¯¯¯¯¯¯¯¯¯QB=1.625cm.


Mathematics
NCERT Exemplar
Standard VI

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