To construct a perpendicular line using a point on the line, the following steps need to be followed:
1. Draw a line that passes through the given point and is perpendicular to the given line.
2. This perpendicular line should intersect the given line at a 90-degree angle.
3. Use a protractor to measure the angle between the given line and the perpendicular line.
4. Divide this angle in half to determine the angle that the perpendicular line should make with the given line.
5. Draw a line at this angle from the given point, and this line will be perpendicular to the given line.