Two or Three Points
This activity belongs to the GeoGebra book GeoGebra Principia.
Now we just have to use those simple tools to investigate a wide variety of situations with their assistance.
From now on, we consider the distances from an arbitrary point X(x,y) to A and B defined as:
XA(x,y):= Distance(X, A)
XB(x,y):= Distance(X, B)
to a line r as:
Xr(x,y):= Distance(X, r)
and to a circle c as:
Xc(x,y):= Distance(X, c)
Equidistance to Two or Three Points
By contracting the circles with the activated trace, at each point in the plane, the color of the nearest center remains, resulting in the perpendicular bisector.
The implicit curve of the perpendicular bisector of AB is given by the equation:
XA – XB = 0
In the case of three points, we can visualize the circumcenter [2] of the triangle they form.
Author of the construction of GeoGebra: Rafael Losada.