Constructing a Perpendicular Line from a Point Not on the Line

Constructing a Perpendicular Line from a Point Not on the Line

How to construct a perpendicular line from a point that is not on the line.

Goal

Constructing a Perpendicular Line from a Point Not on the Line: Goal

Goal:
Constructing the line
that is perpendicular to the given line
and that passes through the given point
which is not on the line.

How to Construct

Constructing a Perpendicular Line from a Point Not 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 Not 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 an arc
that is below the given point.
(red arc)

Constructing a Perpendicular Line from a Point Not 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 an arc (red arc)
that intersects the previous arc (blue arc).

Constructing a Perpendicular Line from a Point Not on the Line: Step 4

Draw a line
that passes through the given point
and the intersecting point 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
which is not on the line.