Medial Curve, Point–Point

mdptpt.html

Exploration

Show that the line is equidistant from the points and .

Approach

Create the points and compute distances to an arbitrary point. Form an equation by setting the distances equal to each other.

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 points.

Clear[x,y,x1,y1,x2,y2];
P=Point2D[x,y];
p1=Point2D[x1,y1];
p2=Point2D[x2,y2];

Form an equation by setting the distances (squared) to the arbitrary point equal to each other.

eq1=Distance2D[P,p1]^2==
    Distance2D[P,p2]^2

Construct a line from the equation and simplify.

Map[Factor,
    Line2D[eq1,{x,y}] //Simplify]