The perpendicular bisector of the straight line joining the two points.
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Points equidistant from AB lie on its perpendicular bisector. Points 5 inches from A lie on the circle with centre A and radius = 5 inches. You will have two points where the perp bisector and circle intersect.
That's a sphere whose radius is the constant equal distance.
Another circle midway between the originals.
No. A line is the locus of all points located between any two points.