2007-10-21 06:44:50 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The point COULD be the midpoint, but there is an entire locus of points (ie the perpendicular bisector) that are also equidistant from the end points. Think of the segment as the base of a triangle, now create a bunch of isosceles triangles with that base. All the points used as the third point of the triangle are equidistant to the endpoints and yet not the midpoint since they're not on the line.
2007-10-21 06:50:28 · answer #1 · answered by math_ninja 3 · 0⤊ 0⤋
The midpoint IS one of the points that is equidistant from the end points of a segment. But there are an infinite number of other points equidistant from the endpoints of the same segment, namely all the points on the perpendicular bisector of the segment.
2007-10-21 13:51:07 · answer #2 · answered by baja_tom 4 · 0⤊ 0⤋
Because it might not be on the segment at all!
If it is on the segment, then it's indeed the midpoint.
And by the way, any answer that talks about THE perpendicular bisector assumes everything is going on in a single plane (i.e., just two dimensions).
2007-10-22 01:15:31 · answer #3 · answered by Curt Monash 7 · 0⤊ 0⤋