Question

Draw a line $l$ and a point $X$ on it. Through $X$ , draw a line segment $\overline{XY}$ perpendicular to $l$. Now draw a perpendicular to $\overline{XY}$ at $Y$. (Use a ruler and compass).

Answer 1

Steps of construction:

Step-1: Draw a line $l$ with a point $X$ on it.

Step-2: Open the arms of the compass to a medium setting (the actual width of the arm does not matter), draw a short arc on each side of point $X$ forming point $A$ and $B$.

Step-3: Place the compass pointer at $A$, set its width to any setting beyond $X$ and draw an arc.

Step-4: Without changing the width of the compass place the pointer at $B$ and draw another arc so that two arcs intersect each other at $Y$.

Step-5: Using a ruler join $X$ and $Y$. Here, $\overline{XY}$ is perpendicular to $l$.

Step-6: Again open the arms of the compass to a medium setting (the actual width of the arm does not matter), and draw a short arc on each side of point $Y$ forming points $C$ and $D$.

Step-7: Place the compass pointer at $C$, set its width to any setting beyond $Y$ and draw an arc.

Step-8: Without changing the width of the compass place the pointer at $D$ and draw another arc so that two arcs intersect each other at $M$.

Step-9: Using a ruler join $M$ and $Y$ to get the required perpendicular at $Y$.