Q1. - Geometry

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 $P$.

Step-by-Step Solution

Answer

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 $l$.