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 andCode:B o * * * * P *-----------* Q

Find another point equidistant from andCode:P *-----------* Q * * o C

If we findallthe points equidistant from and (zillions of them),

. . they form the perpendicular bisector of segmentCode:o o o o o o P *-----o-----* Q o o o