Exploring Analyic Geometry with Mathematica®

Home Contents Commands Packages Explorations Reference
Tour Lines Circles Conics Analysis Tangents

Collinear Points

ptscol.html

Exploration

Show that the three points (3a,0), (0,3b) and (a,2b) are collinear.

Approach

Three points "ptscol_1.gif", "ptscol_2.gif" and "ptscol_3.gif" are collinear if the determinant

"ptscol_4.gif"

is zero.

Initialize

To initialize Descarta2D, select the input cell bracket and press SHIFT-Enter.

This initialization assumes that the Descarta2D software has been copied into one of the standard directories for AddOns which are on the Mathematica search path, $Path.

<<Descarta2D`

Solution

Use the Mathematica Det command to evaluate the determinant.

Clear[a,b];
Det[{{3a,0,1},
     {0,3b,1},
     {a,2b,1}}]

"ptscol_5.gif"

Discussion

The function IsCollinear2D also reveals if three points are collinear.

IsCollinear2D[
   p1=Point2D[3a,0],
   p2=Point2D[0,3b],
   p3=Point2D[a,2b]]

"ptscol_6.gif"

This is the plot of a numerical example.

Sketch2D[{p1,p2,p3,
          Line2D[p1,p3]} /. {a->2,b->1.75}]

"ptscol_7.gif"

Graphics saved as "ptscol01.eps".


Copyright © 1999-2007 Donald L. Vossler, Descarta2D Publishing
www.Descarta2D.com