I think you have this in reverse- the set of points which are equidistant from two points A and B is of course the perpendicular bisector (this is often used as the definition of a line). But the distance from point A to a line is understood to be the minimum (orthogonal) distance. If A and B are the same distance from a line, their orthogonal distances to the line are equal.Stuart Kovinsky wrote: I disagree. A point which is equidistant from two other points does not need to be a perpedicular bisector; however, a line can only be described as equidistant from two points if the entire line is equidistant, and that will only be the case if the line is a perpendicular bisector of the line joining the two points in question; otherwise, one point on the line may be equidistant but all of the other points on the line won't be.
Mind you, this is a completely academic discussion, of no relevance to the GMAT. I've never seen a real GMAT question that required the test-taker to even know what 'distance from a point to a line' means, and as this discussion demonstrates, the phrase could, quite reasonably, be interpreted in different ways. This question fails to be a realistic GMAT question on two counts- it tests a definition test-takers would not be assumed to know, and it still has two correct answers even if you divine the interpretation intended by the question writer.
