Question

Draw a figure roughly like one shown, but larger. Do the indicated construction clearly enough so that your method can be understood easily.

The perpendicular to $l$ at $P$.

Short answer

A line $l$with a point $P$on it.

Step-by-step solution

Step 1. Given information.   

A line $l$with a point $P$on it.

Step 2. Concept used.

Draw by using compass.

Step 3. Construction.

The following steps are to be followed for constructing a line perpendicular to the given line at a given point:

a). Construct a line $l$of some definite length (say 5 cm) and mark point $P$arbitrarily as shown below:

b). Now, using a compass, with $P$as center and any radius within the length of the line, draw arcs on both sides of the point. The points are marked as$A and B$:

c). Now, with point $A$as center, and radius greater than the measure of $AP$, draw an arc as shown below. Repeat the same process with $B$as center and keeping the radius as same to meet the first arc to obtain a new point$C$:

c) Joining the points $C$and $P$gives the segment $PC$which forms the perpendicular to the given line $l$.