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A and B are two fixed points in a plane. A point moves so that it is always the same distance from A as it is from B. Which statement about its path is TRUE?

Competition practiceGeometry
  • AThe path is the circle having AB as its diameter
  • BThe path is the straight line AB itself
  • CThe path is the perpendicular bisector of AB
  • DThe path is a pair of straight lines parallel to AB

Step-by-Step Solution

Every point of the perpendicular bisector of AB is equidistant from A and B, and conversely any point equidistant from A and B lies on it. So the locus is exactly the perpendicular bisector of the segment AB.
Answer: C) The path is the perpendicular bisector of AB

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