.: Perpendicular bisector :.
Perpendicular bisector:
A perpendicular bisector of two points A and B is the geometric place that
are equidistant of A and B.
m := { P: ||P-A||=||P-B|| }
Resume
The presented construction uses both intersection points of the 2 circumferences defined by the
2 given points, A and B.
Briefly the algotrithm is:
given the points A and B
1: c0:= Circumference ( A,B )
2: c1:= Circumference ( B,A )
3: C:= IntersectionPoint_south ( c0,c1 )
4: D:= IntersectionPoint_north ( c0,c1 )
5: m:= Line ( C,D )
6: Distance_1 := ||A-m|| = x
7: Distance_2 := ||B-m|| = x
Construction's details
- Given A and B, build the circumferences c0 and c1,
c0 of center in A and passing by B and
c1 of center in B and passing by A.
- Build the points C and D, intersection between c0 and c1
(note that we can choose a direction with the circumferences and with that is possible
distinguish, for example, C as "intersection north" and D as "intersection south" -
internally iGeom does this).
- Build the line m defined by the points C and D. This line has the desired property,
in other words, it is the perpendicular bisector (try to prove this mathematical result).
Interactive construction
We present below the construction proposed above inside iGeom.
Move the point A (or B) and observe that the line m is (without numeric errors)
eauidistant of the points A and B.
To move a point, the button "move" must be selected
.
