Let be a line segment in a plane (we are assuming the Euclidean plane). A bisector of is any line that passes through the midpoint of . A perpendicular bisector of is a bisector that is perpendicular to .
It is an easy exercise to show that a line is a perpendicular bisector of iff every point lying on is equidistant from and . From this, one concludes that the perpendicular bisector of a line segment is always unique.
use a compass to draw the circle centered at point with radius the length of , by fixing one end of the compass at and the movable end at ,
similarly, draw the circle centered at with the same radius as above, with the compass fixed at and movable at ,
and intersect at two points, say (why?)
with a ruler, draw the line ,
then is the perpendicular bisector of .
(Note: we assume that there is always an ample supply of compasses and rulers of varying sizes, so that given any positive real number , we can find a compass that opens wider than and a ruler that is longer than ).
One of the most common use of perpendicular bisectors is to find the center of a circle constructed from three points in a Euclidean plane:
|Date of creation||2013-03-22 16:29:03|
|Last modified on||2013-03-22 16:29:03|
|Last modified by||CWoo (3771)|