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Mathematics

Draw a line segment PQ\overline{PQ} of length 6.8 cm. Draw a perpendicular to it from a point A outside PQ by using a ruler and compass.

Constructions

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Answer

Steps:

  1. Draw a line segment PQ\overline{PQ} of length 6.8 cm.

  2. Mark a point A outside the line segment PQ\overline{PQ}.

  3. With A as centre and any suitable radius, draw an arc to cut PQ\overline{PQ} or the line containing PQ\overline{PQ} at points C and D.

  4. With C and D as centres, draw two arcs of equal radius (>12CD)\left(\gt\dfrac{1}{2}\text{CD}\right) cutting each other at the point Q' on the other side of PQ.

  5. Join A and Q'. Let AQ' intersect PQ at N.

Draw a line segment PQ of length 6.8 cm. Draw a perpendicular to it from a point A outside PQ by using a ruler and compass. Practical Geometry (Constructions), ML Aggarwal Understanding Mathematics Solutions ICSE Class 6.

Hence, AN is the required perpendicular from point A to the line segment PQ\overline{PQ}.

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