Question

Draw a line $\text{'}l\text{'}$ and mark any point $P$ on it. Through this point construct a line perpendicular to $\text{'}l\text{'}$ by:

Using a ruler and compass

Answer 1

Steps of construction:

Step-1: Construct a line $\text{'}l\text{'}$ with point $P$ on it.

Step-2: Open the arm of the compass to a medium setting on the line $\text{'}l\text{'}$.

Step-3: Without changing the compass setting draw an arc on the line at each side of the point $P$ forming points $A$and $B$.

These two points are thus at the same distance from $P$.

Step-4: Put the compass pointer at $A$, and set its width to any setting beyond $P$.

Step-5: Draw an arc on one side of the line keeping pointer at $A$ .

Step-6: Without changing the setting of the compass place the pointer at $B$ and draw another arc so that two arcs intersect each other. Mark this point as $Q$.

Step-7: Using a ruler join $P$ and $Q$ to get the required perpendicular.