GCSE Maths Practice: loci-and-constructions

Question 4 of 10

This question teaches the locus of points equidistant from two points.

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\( \begin{array}{l}\text{What shape is formed by the locus of points equidistant from two fixed points?}\end{array} \)

Choose one option:

Use compass to draw arcs from both points, then connect intersections to form the perpendicular bisector.

The set of all points equidistant from two fixed points forms a straight line perpendicular to the segment joining the points, called the perpendicular bisector. Students should practise constructing this using a compass and ruler, drawing arcs above and below the line and connecting intersection points. Understanding this locus is crucial for geometric constructions, proofs, and triangle properties. Visualisation helps internalise equidistance concepts. Mastery of perpendicular bisectors prepares students for complex constructions, including circumcenters and triangle optimisation problems. Regular practice ensures proficiency in classical constructions and strengthens geometric reasoning.