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 $l$.

To do: To 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 $l$.
 

Steps of construction:

• Draw a line l, take a point P on it. Draw a perpendicular passing through point P.
• Now adjust the compass up-to-the length of 4 cm. Taking P as the center, draw an arc to intersect this perpendicular at point X.
• Choose any point Y on line l, join X to Y.
• Taking Y as a center and with a convenient radius, draw an arc intersecting l at A and XY at B.
• Taking X as a center and with the same radius as above, draw an arc CD cutting XY at E
• Adjust the compass up-to to the length of AB.
• Hence, line m is parallel to line l at a distance of 4 cm.
• Without changing the opening of the compass and taking E as the center, draw an arc to intersect the previously drawn arc CD at F.
• Join the points X and F to draw a line m.

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Updated on: 10-Oct-2022

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