Exploring Analyic Geometry with Mathematica®

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Intersection of Lines in Intercept Form

intrsct.html

Exploration

Show that the point of intersection of the lines

"intrsct_1.gif" and "intrsct_2.gif"

is

"intrsct_3.gif".

Approach

Create the two lines and intersect them.

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

Create the two lines.

Clear[a,b];
l1=Line2D[{a,0},{0,b}];
l2=Line2D[{b,0},{0,a}];

Intersect the lines.

Point2D[l1,l2] //Simplify

"intrsct_4.gif"

Discussion

Notice that the formula cannot be used if a=±b, because in both cases the two lines are coincident. This limitation is more obvious if we do not simplify the equation for the point of intersection (the denominators are zero when a=±b).

Point2D[l1,l2]

"intrsct_5.gif"


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