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Construction - Perpendicular to a Line

Construction - Perpendicular to a Line

Geometric construction uses a pencil, ruler and a pair of compasses. Mark points A and B near each end of the line. From point A, draw short arcs above and below the line. Repeat for point B, so that the arcs intersect.

The perpendicular line is the line joining the points where both arcs cross.

The perpendicular line will bisect (divide equally into two) the line between the points used to draw the arc (i.e. the perpendicular will be halfway along AB). This is known as a Perpendicular Bisector.

Example 1

Draw a vertical line at least 8 cm long. Draw a horizontal line that is perpendicular to the drawn line.

How to do it: from a point near the left hand end of the line (marked A), draw an arc above the line using a pair of compasses. Without changing the setting of the compasses, and from the same point, draw an arc below the line;

Drawing a perpendicular line: first arcs

from a point (B) toward the right hand end of the line, draw similar arcs above and below;

Drawing a perpendicular line: second arcs

join the two intersection points C-D for a perpendicular line.


Drawing a perpendicular line: completing the bisector

Example 2

Draw a vertical line at least 8 cm long. Construct a perpendicular to this line.

Draw a perpendicular line as before, but in this instance the perpendicular line will be horizontal.


Drawing a horizontal perpendicular line