Question

Question 2

Given some line segment $\overline{AB}$, whose length you do not know, construct $\overline{PQ}$ such that the length of $\overline{PQ}$ is twice that of $\overline{AB}$.

Answer 1

Steps of construction:
(i) Given $\overline{AB}$ whose length is not known.

(ii) Fix the compasses pointer on A and the pencil end on B. The opening of the instrument now gives the length of $\overline{AB}$.

(iii) Draw any line '$l$'. Choose a point P on '$l$'. Without changing the compasses setting, place the pointer on Q.

(iv) Draw an arc that cuts '$l$' at a point R.

(v) Now place the pointer on R and without changing the compasses setting, draw another arc that cuts '$l$' at a point Q. Hence, $\overline{PQ}$ is the required line segment whose length is twice that of AB.