# Shortest Distance between a Point and a Line in 2D

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This Demonstration shows how the scalar product (dot product) can be used to find the point of shortest distance between a point P and a line. You can modify the line by dragging points A and B.

Contributed by: Sergio Hannibal Mejía (Yokohama International School) (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

This Demonstration is intended for teachers trying to illustrate how the inner product (dot product) - )· becomes zero when the point X on the line AB is closest to the point P. The Demonstration can be used as an interactive board; teachers can keep their students' attention on a given element by not displaying other elements.

## Permanent Citation

"Shortest Distance between a Point and a Line in 2D"

http://demonstrations.wolfram.com/ShortestDistanceBetweenAPointAndALineIn2D/

Wolfram Demonstrations Project

Published: March 7 2011