To find: The set of points in space that are equidistance from
Answer to Problem 47PPS
The set of point in space that are equidistance from
Explanation of Solution
Given information:
The given
Figure (1)
Proof:
If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. (Converse of the perpendicular bisector theorem)
In a plane, converse of the perpendicular bisector theorem shows the set of all points is the perpendicular bisector of the segment.
View the 3-space as a rotation of the plane through the segment around the line through the segment. Then, the perpendicular bisector (line) of the segment will generate a perpendicular bisector (plane) of the segment as shown in figure (2).
Figure (2)
Therefore, the set of point in space that are equidistance from
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