AQA•GCSE•Mathematics•Geometry & Measures
Loci
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Sample Questions
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EasyQuestion 1
[2 marks]Describe the locus of points that are exactly 4 cm from a fixed point P.
Solution for Question 1
MediumQuestion 2
[3 marks]Points A and B are 6 cm apart.
Describe the locus of points that are equidistant from A and B.
Solution for Question 2
HardQuestion 3
[4 marks]A rectangular garden ABCD measures 10 m by 8 m.
A tree must be planted so that it is:
- More than 3 m from corner A
- Closer to AB than to AD
Describe how to find the region where the tree can be planted.
Solution for Question 3
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Generate Unlimited QuestionsAbout Loci in AQA GCSE
A locus (plural: loci) is a set of points satisfying a given condition. The main types are: fixed distance from a point (circle), fixed distance from a line (parallel lines), equidistant from two points (perpendicular bisector), equidistant from two lines (angle bisector).
When multiple conditions apply, the solution is where all loci meet. For "closer to A than B," shade the region on A's side of the perpendicular bisector of AB. For "within 3 cm of point P," shade inside a circle radius 3 cm centred at P.
In exam questions, shade or mark the required region clearly. Show construction lines for full marks.
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