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Question

Question 4

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

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Solution

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 ¯¯¯¯¯¯¯¯AB which cuts it at C. Thus, C is the midpoint of ¯¯¯¯¯¯¯¯AB.
(iii) Draw the perpendicular bisector of ¯¯¯¯¯¯¯¯AC which cuts it at D. Thus D is the midpoint of.
(iv) Again, draw the perpendicular bisector of ¯¯¯¯¯¯¯¯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 ¯¯¯¯¯¯¯¯AB in the four equal parts.
(vi) By actual measurement, we find that ¯¯¯¯¯¯¯¯¯AD=¯¯¯¯¯¯¯¯¯DC=¯¯¯¯¯¯¯¯CE=¯¯¯¯¯¯¯¯EB=3.2cm


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