Question

Draw a line $l$. Draw a perpendicular to $l$ at any point on $l$. On this perpendicular choose a point $X$, $4cm$ away from $l$. Through $X$, draw a line $m$ parallel to $l$.

Answer 1

Steps of constructions:

1. Draw a line $l$ mark a point on it.

2. With $P$ as center draw an arc intersects the line at $A$ and $B$.

3.With $A$ as center and radius is more than $AP$ draw an arc, with $B$ as center and radius is more than $AP$ draw another arc.

4. Mark the point of the intersection of the arcs is $Q$ and join $PQ$

5. Mark a point $X$ on $PQ$ such that $PQ=4cm$ with help of compass.

6. with $P$ as center draw an arc intersects $l$ at $C$, $PQ$ at $D$.

7.With $X$ as center and same radius draw the arcs as before, intersects $PQ$ at $E$.

8.Take the length of the arc $CD$ and draw the arc at center $E$ which cuts at $F$.

9. Draw a line passing through the points $F$ and $X$.

Hence, the line $m$ is required line.

Since, $\angle FXE=\angle CPE$ [Alternate interior angles are equal]

$PX=4cm$