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Mathematics

Draw a line segment of length 8.8 cm. Using ruler and compass, divide it into four equal parts. Verify by actual measurement.

Constructions

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Answer

Steps:

  1. Draw a line segment AB\overline{AB} of length 8.8 cm.

  2. Construct the perpendicular bisector of AB. Let it meet AB at the point M. Then M is the mid-point of AB, so AM = MB = 4.4 cm.

  3. Construct the perpendicular bisector of AM. Let it meet AM at the point N. Then N is the mid-point of AM, so AN = NM = 2.2 cm.

  4. Construct the perpendicular bisector of MB. Let it meet MB at the point O. Then O is the mid-point of MB, so MO = OB = 2.2 cm.

Draw a line segment of length 8.8 cm. Using ruler and compass, divide it into four equal parts. Verify by actual measurement. Practical Geometry (Constructions), ML Aggarwal Understanding Mathematics Solutions ICSE Class 6.

Thus, the line segment AB\overline{AB} is divided into four equal parts AN, NM, MO and OB.

On measuring with a ruler, we find AN = NM = MO = OB = 2.2 cm.

Hence, the line segment AB\overline{AB} has been divided into four equal parts, each of length 2.2 cm.

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