Orthopolar Lines for a Quadrilateral

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Four given points form the quadrilateral and its diagonals and . The lines are two-colored to give triangles , , , and .


Drop gray perpendiculars from the vertices of to the blue line to obtain new points . The cyan perpendiculars to , to and to are concurrent at the cyan orthopole. The orthopoles of the four component triangles of the quadrilateral are collinear, forming the black orthopolar line. If this construction is repeated, the red orthopolar line of the black orthopolar line is parallel to the original line .

You can drag the vertices of and two locators on the green line to move it.


Contributed by: Ed Pegg Jr (May 2018)
Open content licensed under CC BY-NC-SA



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.