Given $ \overline{\mathrm{AB}} $ of length $ 7.3 \mathrm{~cm} $ and $ \overline{\mathrm{CD}} $ of length $ 3.4 \mathrm{~cm} $, construct a line segment $ \overline{X Y} $ such that the length of $ \overline{X Y} $ is equal to the difference between the lengths of $ \overline{\mathrm{AB}} $ and $ \overline{\mathrm{CD}} $. Verify by measurement.
Given $\overline{AB}$ of length $7.3\ cm$ and $\overline{CD}$ of length $3.4\ cm$.
To do:
We have to construct a line segment $\overline{XY}$ whose length is equal to the difference between the lengths of $\overline{AB}$ and $\overline{CD}$ and verify it by measurement.
Solution:
Steps of construction:
(i) First let us take compasses and by pointing the pointer of the compasses at point C of the line segment CD let us take the length of the line segment CD with compasses.
(ii) Now, by placing the pointer of the compasses on point A of the line segment AB let us draw an arc and point it as P.
(iii) let us draw the line 'l' and mark a point X on it.
(iv) let us adjust the compasses up to the length of PB, by pointing the pointer of compasses on point X let us draw an arc on the line 'l' and point it as point Y.
(v) Therefore, The line segment $\overline{XY}$ is formed.
(vi) The difference between the lengths of $\overline{AB}$ and $\overline{CD}$ is $7.3\ cm - 3.4\ cm = 3.9\ cm$.
(vii) We can verify the measurement by placing the ruler's starting point on point X to point Y measures $3.9\ cm$.
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