# Construct a perpendicular line through a point that does not lie on any line.

A line that makes a 90-degree angle with another line is called perpendicular to that line.

## Answer: Let's look into the construction of a perpendicular line through a point that does not lie on any line.

We need to make use of a compass and a ruler to construct the perpendicular line.

**Explanation:**

Given below are the steps of construction:

Given: A line and a point P that does not on the line.

- Adjust the compass in such a way that its opening is greater than the perpendicular distance from the point P to the line
- Keeping the compass at point P, using this measure scribe two arcs intersecting the line at two different points as shown below.

- Let the two points be A and B. Adjust the compass to a particular radius and cut two arcs keeping the compass at points A and B respectively on the other side of the line opposite to point P.
- Let the point where the two arcs meet be called as Q as shown in the figure.

- Join the points P and Q as shown below.