question_answer

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 such that length of \[\overline{PX}\]= length of \[\overline{AB}\],  then cut off \[\overline{XQ}\], such that \[\overline{XQ}\] also has the length as \[\overline{AB}\],).

Answer:

Given \[\overline{AB}=3.9\text{ }cm\]. Now, to construct required line segment by using compasses, we use the following steps:

Step I: Firstly, draw \[\overline{AB}=3.9\text{ }cm\]

Step II: Now, to draw an another line l, mark a point P on it.

Step III: Place the pointer of compasses at the zero mark of the ruler. Open it to the place of the pencil point up to 3.9 cm mark.

Step IV: Without changing the opening of the compasses, place the pointer on P and swing an arc to cut l at X.

Step V: Measure \[\overline{PX}\], we get \[\overline{PX}=3.9\text{ }cm\]

\[=\overline{AB}\].

Step VI: Again, without changing the opening of the compasses, place the pointer on X and swing an arc to cut l at Q.

Step VII: Now, measure \[\overline{XQ}\], we get \[\overline{XQ}=3.9\]\[cm=\overline{AB}\] .

Step VIII: \[\overline{PQ}=\overline{PX}+\overline{XQ}=(3.9+3.9)\text{ }cm\]

\[=\overline{AB}+\overline{AB}=2\overline{AB}\] Hence, \[\overline{PQ}\] is twice that of \[\overline{AB}\] .

Verification: On measuring the length of \[\overline{PQ}\] and \[\overline{AB}\] we get, \[\overline{PQ}=7.8\text{ }cm\] and \[\overline{AB}=3.9\text{ }cm\] and \[\overline{PQ}=2(\overline{AB})=7.8\text{ }cm\]Thus, twice of \[\overline{AB}\] is equal to \[\overline{PQ}\].