lesson
A locus is a set of permitted positions
1 · Learn
Points a fixed distance from a point form a circle. Points equidistant from two distinct points lie on their perpendicular bisector. A locus describes every position satisfying a condition, not one guessed location.
When two conditions must both hold, find their intersection. State whether boundaries are included when inequalities describe a region.
2 · Worked example
A point 3 cm from A and equally distant from A and B must lie both on the radius-3 circle centred at A and on the perpendicular bisector of AB.
3 · Your turn
What is the locus of points exactly 4 cm from a fixed point P?
Check your answer
A circle centred at P with radius 4 cm, not the whole filled disc.
4 · Apply your learning
Draw AB=4 cm with safe construction instruments. Construct the circle of radius 3 cm centred at A and the perpendicular bisector of AB. Mark EVERY intersection. Explain why the points satisfy both distance conditions and why there are two in this construction.
Adult guidance and safety
Require reasoning and a check. Provide accurate graphs, construction instruments and varied practice. Annual KS3 allocation is proposed; do not treat these short models as a complete assessed programme.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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