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Question
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.
Solution
- Given that, `overline"AB"` = 7.3 cm and `overline"CD"` = 3.4 cm
- Adjust the compasses up to the length of CD and put the pointer of the compasses at A. Draw an arc to cut AB at P.
- Adjust the compasses up to the length of PB. Now draw a line l and mark a point X on it.
- Now, putting the pointer of compasses at point X, draw an arc to cut the line at Y.
`overline"XY"` is the required line segment.
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(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"`.)
