Education Technology

Shortest Distance Between Points and Lines

Published on 06/09/2008

Activity Overview

This activity investigates concepts such as the shortest distance between two points in a plane, and the shortest distance between a line and a point not on the line. The analytical explanation of these concepts is supported with visual illustrations.

Before the Activity

  • Install the Cabri Jr. App on the students' graphing calculators using TI-Connect™, a TI Connectivity Cable and the Unit-to-Unit Link Cable
  • Use the TI-Navigator™ to transfer the attached Cabri Jr. AppVar files to each calculator
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 27 - 30 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to your class.

    Follow the Activity procedures:

  • Use the AppVar to go directly to the exploration section
  • Draw two segments sharing an endpoint
  • Measure the lengths of the two segments and find the sum
  • Drag the point on the segments until the sum of the segments is at its lowest possible value
  • Understand how the shortest distance between two points is a straight line
  • Draw a line, a point not on the line, and a segment connecting them
  • Find the location of the point on the line such that the length of the segment is the shortest
  • Draw a line, two points not on the line, and segments that connect the points to one point on the line
  • Note the relationship between the angles formed when the sum of the segments is minimum
  • After the Activity

    Review student results:

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