GCSE Maths Practice: loci-and-constructions

Question 9 of 10

This question teaches the locus of points a fixed distance from a straight line.

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\( \begin{array}{l}\text{Describe the locus of points exactly 2 cm away from a straight line.}\end{array} \)

Choose one option:

Draw two parallel lines on each side of the given line, each at the specified distance.

For any straight line, points at a fixed distance from it lie on two parallel lines, one on each side of the original line. This distance is consistent for all points, forming parallel lines equidistant from the original. Understanding this locus is crucial for constructions, coordinate geometry, and interpreting distance conditions. Students should practise visualising and drawing these loci using ruler and compass, reinforcing geometric intuition. Recognising patterns in loci prepares students for more advanced problems involving circles, bisectors, and perpendicular bisectors. Practise will develop both conceptual understanding and practical construction skills.