The locus of points equidistant from two given points is which geometric object?

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The main idea is that the set of points that are the same distance from two fixed points is the perpendicular bisector of the segment joining them. If you take the segment connecting the two points and find its midpoint, the line through that midpoint that is perpendicular to the segment consists of all points X for which XP = XQ. This happens because that line is the axis of symmetry swapping the two fixed points, so any point on it sees the two fixed points at equal distances. Conversely, if a point has equal distances to the two fixed points, it lies on that same line. Therefore, the locus is the perpendicular bisector of the segment joining the two points. The other options describe different objects and do not capture the condition of equal distances.