question_answer

Given \[\overline{AB}\] of length 7.3 cm and \[\overline{CD}\] of length 3.4 cm, construct a line segment \[\overline{XY}\] such that the length of \[\overline{XY}\] is equal to the difference between the lengths of \[\overline{AB}\] and \[\overline{CD}\]. Verify by measurement.

Answer:

Given, \[\overline{AB}=7.3\text{ }cm\] and \[\overline{CD}=3.4\text{ }cm\]

Now, to construct required line segment \[\overline{XY}\], we use the following steps:

Step I: Firstly, draw \[\overline{AB}=7.3\text{ }cm\] and \[\overline{CD}=3.4\text{ }cm\]

Step II: Now, place the pointer of compasses on C of pencil on D. The opening of the instrument gives the length of \[\overline{CD}\] i.e., 3.4 cm.

Step III: Without changing the opening of the compasses place the pointer on A and swing an arc to cut \[\overline{AB}\] at R.

Step IV: Thus, \[\overline{AR}=3.4\text{ }cm\] and \[\overline{RB}\] is the difference between the length of \[\overline{AB}\] and \[\overline{CD}\].

Step V: Now, draw a line I and mark a point X on it.

Step VI: Place the pointer of compasses on R and of pencil on B. The opening of the compasses gives the length of \[\overline{RB}\] .

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

Thus, \[\overline{XY}\] is a line segment whose length is equal to the difference between the lengths of \[\overline{AB}\] and \[\overline{CD}\].

Verification: By actual measurement, we have \[\overline{XY}=3.9\text{ }cm\]

Now, \[\overline{AB}\overline{CD}=7.3\text{ }cm3.4\text{ }cm=3.9\text{ }cm\]

\[\Rightarrow \]        \[\overline{XY}=\overline{AB}\overline{CD}\].

i.e., length of \[\overline{XY}=\] The difference of length of \[\overline{AB}\] and \[\overline{CD}\].                                     Hence, verified.