Education Technology

Finding the Shortest Path

Published on 12/20/2005

Activity Overview

Students discover the shortest distance light travels from an object to the human eye, as the light from the object reflects off a single mirror.

In the process they learn about reflection in a line, congruent angles, angle bisectors, congruent line segments, and perpendicular bisectors.

This Activity comes from SIMMS Integrated Mathematics Level 1, © Kendall/Hunt Publishing Company.

Before the Activity

Print the ShortestPath.SE.pdf file for each student.

Print a teacher copy of the ShortestPath.TE.pdf file, as it provides sample answers to the questions posed.

During the Activity

In Exploration 2, students will use the TI-89 calculator and The Geometer's Sketchpad® App to investigate the path that light travels from an object to a mirror and then to the human eye.


Students will make a conjecture about that shortest distance and answer other questions in Discussion 2, designed to deepen their understanding of the mathematics.


Exploration 2 can be done individually or in pairs. Discussion 2 can be done individually, in small groups, or assigned as homework.


A whole class discussion of student responses is helpful to ensure students fully understand the mathematics involved.

After the Activity

Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary