GCSE Maths Practice: loci-and-constructions

Question 7 of 10

This question introduces the locus of points within a fixed distance from a point.

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\( \begin{array}{l}\text{Describe the locus of points less than 5 cm from a given point.}\end{array} \)

Choose one option:

Use a compass to draw a circle centered at the point with radius 5 cm; the interior represents all points less than 5 cm away.

The locus of points less than 5 cm from a given point forms the interior of a circle with radius 5 cm. All points satisfy the distance condition from the center. This concept is foundational for constructions, loci problems, and geometric proofs. Practising drawing such loci improves spatial reasoning, precision, and understanding of distance conditions. Students should visualise and sketch the circle, labelling key points and verifying distances. Mastery of this concept is essential for more complex loci involving multiple points, intersections, and constraints.