# Activities

• • • ##### Subject Area

• Math: Geometry: Vectors

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• TI-92 Plus / Voyage™ 200
• ##### Software

Cabri Geometry™

• String
• ##### Report an Issue

Trivialization and Dynamisation

#### Activity Overview

This activity will illustrate how classic exercises from elementary vector geometry can be solved using the Computer Algebra System CAS tool.

#### Before the Activity

• Install the Cabri Geometry™ software on the computer
• See the attached PDF file for detailed instructions for this activity
• Print pages 1 - 10 from the attached PDF file for the class
• #### During the Activity

Distribute the pages to the class.

• Use Cabri Geometry to draw an ellipse
• Determine the equation of the ellipse and convert it into the standard form
• Solve the ellipse equation and draw the functions for some values of the variables
• Satisfy the equation and draw the parametric representation of the ellipse
• Perform the above steps manually (by hand), compare the results with those from CAS
• Examine the different solution methods provided on the activity sheet

• Study the vectorial representation of two points and the straight line
• Determine all points on the straight line with a certain ratio
• Replace a component in the direction vector of the straight line by a variable
• Determine values of the variable which results in one, two, or no solutions
• Find the locus of the intersection points and determine its characteristic quantities
• Write the equation of the locus
• #### After the Activity

Students complete the exercises listed on the activity pages.

Review student results.

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