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

The rough figure of the construction will be as follows:

The steps for construction are given below:

Step 1: Draw a line $l$.

Step 2: Mark any point $P$ on line $l$.

Step 3: Now at point $P$, draw a perpendicular line $n$.

Step 4: Place the pointed tip of the compass at $P$ and adjust the compass up to length of $4cm$, draw an arc to cut this perpendicular at point $x$.

Step 5: At point $x$, again draw a perpendicular line $m$ to line $n$, such that it is parallel to $l$.

Therefore, the line thus formed is parallel to $l$ and the distance between the two lines is $4cm$.