Education Technology

# Activities

• ##### Subject Area

• Math: Geometry: Points, Lines and Angles

9-12

90 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 5 from the EXPLORATIONS Book:
Cabri™ Jr.: Interactive Geometry Activities and Investigations.

## Shortest Distance Between Points and Lines

#### 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.

• 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