Constructing a Perpendicular Line from a Point on the Line

Constructing a Perpendicular Line from a Point on the Line

How to construct a perpendicular line from a point that is on the line.

Goal

Constructing a Perpendicular Line from a Point on the Line: Goal

Goal:
Constructing the line
that is perpendicular to the given line
and that passes through
the given point on the given line

How to Construct

Constructing a Perpendicular Line from a Point on the Line: Step 1

Place the point of the compass
at the given point.
(red point)

Draw two arcs
that intersect with the given line.
(red arcs)

Constructing a Perpendicular Line from a Point on the Line: Step 2

Place the point of the compass
at one of the intersection
of the arc and the given line.
(red point)

Draw two arcs
that is above and below the given point.
(red arcs)

Constructing a Perpendicular Line from a Point on the Line: Step 3

Without changing the radius of the compass,
place the point of the compass
at the other intersecting point.
(red point)

Draw two arcs (red arcs)
that intersect the previous arcs (blue arcs).

From this part, it's like
constructing the midpoint of a line segment.

Constructing a Perpendicular Line from a Point on the Line: Step 4

Draw a line
that passes through the intersecting points
formed by the arcs.

Then the vertical line is the line
that is perpendicular to the given line
and that passes through
the given point on the line.