The locus of all points that are the same distance from two given points is a _____.

The locus of all points that are equidistant from two given points is a perpendicular bisector of the line segment joining the two points. This geometric concept arises from the definition and properties of distances in Euclidean geometry.

To elaborate, if you have two points, say $A$ and $B$, the perpendicular bisector is a straight line that not only divides the segment $AB$ into two equal halves but also meets the segment at a right angle (90 degrees). Any point on this line maintains an equal distance to both $A$ and $B$. Thus, if you want to find all such points that are the same distance from both $A$ and $B$, you would need to locate this perpendicular bisector.

In conclusion, the answer is that this locus is a perpendicular bisector.