Question

Given `overline"AB"` of length 3.9 cm, construct `overline"PQ"`  such that the length of `overline"PQ"` is twice that of `overline"AB"`. Verify by measurement.

(Hint: construct `overline"PX"` such that length of `overline"PX"` = length of  `overline"AB"`; then cut off  `overline"XQ"` such that `overline"XQ"` also has the length of `overline"AB"`.) 

Answer 1

A line segment `overline"PQ"` can be drawn such that the length of  `overline"PQ"` is twice that of `overline"AB"` as follows. 

1. Draw a line l and mark a point P on it and let AB be the given line segment of 3.9 cm.
2. By adjusting the compasses up to the length of AB, draw an arc to cut the line at X, while taking the pointer of compasses at point P.
   

3. Again put the pointer on point X and draw an arc to cut line l again at Q.
   
   `overline"PQ"` is the required line segment. By ruler, the length of `overline"PQ"` can be measured which comes to 7.8 cm.