GCSE Maths Practice: loci-and-constructions

Question 10 of 10

This question introduces loci of points equidistant from two parallel lines.

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\( \begin{array}{l}\text{A locus of points equidistant from two parallel lines forms what shape?}\end{array} \)

Choose one option:

Visualise the distance from both lines and draw a line midway between them.

A locus is a set of points satisfying a condition. For two parallel lines, the midpoint locus is another line parallel to the given lines and exactly halfway between them. Understanding loci helps with geometric constructions, map work, and algebraic interpretation of geometric conditions. Practising drawing loci reinforces the concept of equidistance and symmetry. Students can visualise this as all points maintaining equal distance from both lines, forming a straight line. Mastery of loci prepares students for problems involving circles, bisectors, and distance-based conditions in coordinate and plane geometry. Drawing diagrams for different loci conditions strengthens spatial reasoning and problem-solving skills.