Equidistant points
Definition: A point P is equidistant from others if it is the same distance from them.
Try this Drag the point P. It will remain equidistant from Q and R.
A point is equidistant from other points if the
line segments
linking it to them are
congruent (same length).
In the figure above as you move any of the three orange points and note
how P always remains the same distance (equidistant) from the other two.
Alternate definition of a line
An alternate definition of a line is the "the set of all points equidistant from two given points".
This line is known as the locus of the point P. In the figure above click "show locus" and
see that the green dotted line is the locus of all points that are equidistant from Q and R  a straight line.
Other point topics
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