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Question
Draw a line l. Draw a perpendicular to l at any point on l. On this perpendicular choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.
Solution
The steps of construction are as follows.
1) Draw a line l and take a point P on line l. Then, draw a perpendicular at point P
2) Adjusting the compasses up to the length of 4 cm, draw an arc to intersect this perpendicular at point X. Choose any point Y on line l. Join X to Y.
3) Taking Y as centre and with a convenient radius, draw an arc intersecting l at A and XY at B.
4) Taking X as centre and with the same radius as before, draw an arc CD cutting XY at E.
5) Adjust the compasses up to the length of AB. Without changing the opening of compasses and taking E as the centre, draw an arc to intersect the previously drawn arc CD at point F.
6) Join the points X and F to draw a line m.
Line m is the required line which is parallel to line l.
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