GCSE · Constructions & loci

Loci & regionsExam-style questions

A locus as the set of points obeying a rule, the four standard loci, and how to combine several conditions — with scale drawings — to shade the region that satisfies all of them at once.

Start practising Read the lesson

11 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The diagram shows a plan of a field with a straight fence and two trees, $A$ and $B$ . The plan is drawn to a scale of $1$ cm to $10$ m.A bird table is to be placed so that it is:

* less than $45$ m from tree $A$ , and * nearer to tree $A$ than to tree $B$ , and * more than $20$ m from the fence.

On the plan, show by shading the region where the bird table can be placed. You must show all your construction lines.
Level 4 · 5 marksTry it
2
A guard dog is attached by a $5$ m chain to a ring that slides freely along a straight rail of length $20$ m, fixed to the ground in a large open yard.Diagram NOT accurately drawn

(a) Describe the region of the yard the dog can reach.

(b) Work out the area of this region. Give your answer correct to 1 decimal place.
Level 4 · 5 marksTry it