GCSE Maths Practice: loci-and-constructions

Question 6 of 10

This question introduces the locus equidistant from two intersecting lines.

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\( \begin{array}{l}\text{What is the locus of points equidistant from two intersecting lines?}\end{array} \)

Choose one option:

Construct angle bisectors of each angle; the intersection points give the locus.

Points equidistant from two intersecting lines lie along the angle bisectors. Each bisector splits one of the angles formed by the intersection equally. Students should practise drawing intersecting lines and constructing angle bisectors using a compass and ruler. Labeling points along the bisectors clarifies the concept. Understanding this locus is essential for geometric constructions, proofs, and triangle problems. Practising these constructions strengthens geometric reasoning, precision, and familiarity with classical ruler-and-compass techniques. Mastery prepares students for complex locus problems involving multiple lines and points.