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Question

# 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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