 # Loci

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A locus (plural loci) refers to all the points which fit a particular description. These points can either belong to a region, a line or both.
Here we have a collection of videos to help GCSE Maths students learn about loci.

Loci 1 - describing and drawing the locus of all points following certain rules.
Examples:
1. Draw the locus of all points which are exactly 5 metres from point P.
2. Draw the locus of all points which are less than 5 metres from point P.
3. Draw the locus of all points which are within 2 metres from the line AB.
4. Draw the locus of all points inside the rectangle which are closer to A than to C.
2. Draw the locus of all points inside the triangle which are closer to the line AB than to the line AC.
More on locus of points following rules, this time when more than one rule is being followed
Examples:
1. A lawn is to be planted inside the garden, at least 4 m from the side of the house and 3 m from the tree (T). Shade the lawn.
2. A rosebed is to be planted within 5 m of A and within 6 m of C. Shade the rosebed.
3. Caroline wants to plant a lawn which is closer to the side AB than AD, and within 6 m of C. Shade her lawn.

GCSE Tutorial Loci and Locus
Examples:
1. Draw
(i) the locus of a point which moves so that it is always exactly 4 cm from the fixed point X and
(ii) the locus of points less than 4 cm from the fixed point X
2. Draw the locus of points no further than 3 cm from A and no further than 4 cm from B.
3. (i) Draw the locus of a point equidistant from the points X and Y.
(ii) Draw the locus of points closer to the point X than to the point Y.
(iii) Draw the locus of points closer to X than to Y but no less than 5 cm from X.
4. Draw the locus of points closer to the AB than the line BC in the rectangle ABCD.
4. A dog is on a lead tethered to a post in the corner of a garden. The lead is 5 m long. A cat is free to roam to all parts of the garden but is not allowed within 3 m of the house by its owner. Show the safe area the cat can safely roam on the diagram below.
GCSE Maths revision Exam paper practice
Loci and scale drawing

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