Question

use the compass and ruler to construct the line perpendicular to the line l through the point p.

Explanation:

Step1: Draw arcs intersecting line \( l \)

Set the compass width. With \( P \) as the center, draw arcs intersecting line \( l \) at two points \( A \) and \( B \).

Step2: Draw arcs from \( A \) and \( B \)

Keep the same compass width. Draw arcs from \( A \) and \( B \) (on the opposite side of \( P \) relative to \( l \)). Let these arcs intersect at point \( Q \).

Step3: Draw the perpendicular line

Use the ruler to draw a line through \( P \) and \( Q \). This line is perpendicular to line \( l \).

Answer:

Follow the above three - step construction process using compass and ruler to get the line perpendicular to \( l \) through \( P \).