Thread: Locus Theorem: (two points)

The locus of points equidistant from two points, P and Q, is the perpendicular bisector of the line segment determined by the two points.

I need the above theorem explained an easier way.

Hello, magentarita!

The locus of points equidistant from two points, and
is the perpendicular bisector of the line segment determined by the two points.

We have two points, and , and the line segment joining them.

Code:

    P *-----------* Q

Find a point equidistant from and
. . That is: .

Code:

            A
            o
           * *
          *   *
         *     *
        *       *
       *         *
    P *-----------* Q

Find another point equidistant from and

Code:

            B
            o
          *   *
        *       *
    P *-----------* Q

Find another point equidistant from and

Code:

    P *-----------* Q
         *     *
            o
            C

If we find all the points equidistant from and (zillions of them),
. . they form the perpendicular bisector of segment

Code:

            o
            o
            o
            o
            o
            o
    P *-----o-----* Q
            o
            o
            o

Originally Posted by Soroban

Hello, magentarita!


We have two points, and , and the line segment joining them.

Code:

 
 
    P *-----------* Q

Find a point equidistant from and
. . That is: .

Code:

            A
            o
           * *
          *   *
         *     *
        *       *
       *         *
    P *-----------* Q

Find another point equidistant from and

Code:

            B
            o
          *   *
        *       *
    P *-----------* Q

Find another point equidistant from and

Code:

 
    P *-----------* Q
         *     *
            o
            C

If we find all the points equidistant from and (zillions of them),
. . they form the perpendicular bisector of segment

Code:

 
            o
            o
            o
            o
            o
            o
    P *-----o-----* Q
            o
            o
            o

Wonderfully done!