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, $\displaystyle P$ and $\displaystyle Q,$
is the perpendicular bisector of the line segment determined by the two points.
We have two points, $\displaystyle P$ and $\displaystyle Q$, and the line segment joining them.Code:P *-----------* Q
Find a point $\displaystyle A$ equidistant from $\displaystyle P$ and $\displaystyle Q.$
. . That is: .$\displaystyle AP \:=\:AQ$Code:A o * * * * * * * * * * P *-----------* Q
Find another point $\displaystyle B$ equidistant from $\displaystyle P$ and $\displaystyle Q.$Code:B o * * * * P *-----------* Q
Find another point $\displaystyle C$ equidistant from $\displaystyle P$ and $\displaystyle Q.$Code:P *-----------* Q * * o C
If we find all the points equidistant from $\displaystyle P$ and $\displaystyle Q$ (zillions of them),
. . they form the perpendicular bisector of segment $\displaystyle PQ.$Code:o o o o o o P *-----o-----* Q o o o