## Exploring Analyic Geometry with |
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Collinear Points

ptscol.html

Exploration

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

Approach

Three points , and are collinear if the determinant

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}}]

Discussion

The function IsCollinear2D also reveals if three points are collinear.

IsCollinear2D[

p1=Point2D[3a,0],

p2=Point2D[0,3b],

p3=Point2D[a,2b]]

This is the plot of a numerical example.

Sketch2D[{p1,p2,p3,

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

Graphics saved as "ptscol01.eps".

www.Descarta2D.com