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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

More Lessons for GCSE Maths

Math Worksheets

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.

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.

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.

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.

Loci and scale drawing

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