JAMB 2011 · UTME · Q31

The perpendicular bisector of a line $XY$ is the locus of a point

Worked solution (try it first)

The perpendicular bisector of $XY$ passes through the mid-point of $XY$ at right angles to it.
Any point on it forms two congruent right-angled triangles with $X$ and $Y$ , so it is the same distance from $X$ as from $Y$ .
That is option D.