A surveyor in Trinidad is marking the locus of points equidistant from two boundary posts P and Q on a sugar cane estate. She constructs several arcs using her compass. The locus will be:

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Question

A surveyor in Trinidad is marking the locus of points equidistant from two boundary posts P and Q on a sugar cane estate. She constructs several arcs using her compass. The locus will be:

Accepted Answer

The perpendicular bisector of line segment PQ — Award 1 mark for identifying that the locus of points equidistant from two fixed points is the perpendicular bisector of the line segment joining them. A is incorrect because a circle would represent points equidistant from a single point, not two points. C is incorrect because parallel lines are not the locus of equidistant points from two fixed points. D is incorrect because an arc does not represent all points equidistant from P and Q.

Answer

A circle with centre at the midpoint of PQ

Answer

An arc with radius equal to PQ

Answer

Two parallel lines on either side of PQ

Answer

The perpendicular bisector of line segment PQ

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