Loci

Objective. Describe and construct loci satisfying distance conditions.

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2. Worked example
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Learn: the key idea

A locus is the set of all points satisfying a given distance or angle condition, often drawn as a line, curve, or region. A locus of points a fixed distance from a point is a circle, while a locus of points equidistant from two points is the perpendicular bisector of the line joining them. For points exactly 3 cm from a fixed point A, the locus is a circle of radius 3 cm centred on A. Always identify whether the condition involves one point, two points, or a line before choosing the right construction.

Worked example

Describe the locus of points that are exactly 4 cm from a fixed point P.

1 $Identify the condition: constant distance from one point$
2 $Recall that this shape is always a circle$
3 $Set the radius equal to the given distance of 4 cm$
4 $The locus is a circle of radius 4 cm centred on P$

Answer: A circle of radius 4 cm centred on P

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Common mistake. Pupils often draw the locus of points equidistant from two points as a circle rather than a straight perpendicular bisector line. Always check whether the condition compares distances from two objects, which needs a bisecting line, not a circle.

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