A point P is equidistant from two fixed points A and B. Which locus does P trace?

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Question

A point P is equidistant from two fixed points A and B. Which locus does P trace?

Accepted Answer

The perpendicular bisector of the line segment AB — The locus of points equidistant from two fixed points A and B is the perpendicular bisector of the segment AB. Option A describes a circle which is not the correct locus. Option B refers to an angle bisector which relates to equidistance from two lines, not two points. Option D, a parallel line, is not equidistant from both endpoints unless it lies exactly at the midpoint, which still doesn't satisfy the full locus.

Answer

A circle centred on the midpoint of AB

Answer

The angle bisector of angle AOB

Answer

The perpendicular bisector of the line segment AB

Answer

A line parallel to AB

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