Your learning journey
Use ruler and compass constructions and interpret loci as sets of points satisfying distance conditions.
Follow the task-specific calculator guidance in Apply. Keyboard - means the same as −. Attempt before opening a scaffold or intentional practice explanation.
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Connect & Check
Locus: set of all points satisfying a condition. Bisect: divide into two equal parts. Perpendicular bisector: line at 90° through a segment midpoint. Construction arcs: retained compass evidence.
Intentional practice feedback after your attempt
90°.
Right angle.
Intentional practice feedback after your attempt
4 cm.
Midpoint distance.
Intentional practice feedback after your attempt
Equal distances to the two points.
The common distance may vary.
Present
Equal-radius arcs from endpoints intersect at points equally distant from both endpoints; their joining line is the perpendicular bisector. To bisect an angle, mark equal distances along its rays, then intersect equal-radius arcs from those marks. Congruent triangles explain the equal angles. Distance from a point to a line is measured along a perpendicular.
Use a sharp pencil, straightedge and compass; leave arcs visible. For a perpendicular from a point, an arc centred there cuts the line twice; bisect that segment and join to the point. At a point on a line, mark equal distances either side, then use equal arcs. For loci, draw each condition separately and retain their intersection.
Optional scaffold
Choose radius greater than 4 cm.
Intentional practice feedback after your attempt
Line through midpoint at 4 cm, perpendicular to AB, with intersecting arcs.
Equal-distance intersections determine the bisector.
Optional scaffold
Keep compass opening equal for paired arcs.
Intentional practice feedback after your attempt
Two 35° angles; construction arcs retained.
Protractor makes the starting angle, not the bisector.
Optional scaffold
A fixed distance is the radius.
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Circle centre P, radius 3 cm.
Only circumference; no interior shading.
Optional scaffold
Consider both sides of the line.
Intentional practice feedback after your attempt
Strip between parallel lines 1 cm each side, including boundaries.
Distance measured perpendicular.
Apply
Optional scaffold
Choose a radius reaching across l.
Intentional practice feedback after your attempt
Arc from P cuts l at X,Y; bisect XY and draw through P to l.
The constructed line is at 90°.
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Two intersections of radius-4 circles centred A and B.
Both conditions must hold.
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Intersect the closed radius-3 disc with the perpendicular bisector of AB.
May be a segment, point or empty, depending on positions.
No calculator needed. Practical construction quality is teacher reviewed. Use a ruler to check distances and a protractor to check right angles after constructing; they do not replace compass evidence.
Apply and extend
Intentional practice feedback after your attempt
One equidistant point is insufficient to locate the bisector line; use two intersections, or one and the known midpoint. Joining A is generally wrong.
A is not equidistant from itself and B.
Intentional practice feedback after your attempt
None; the two circles are separated since 3+3<8.
Maximum total reach is 6 cm.
Access, Scaffold, Core and Stretch support the same goal. Stretch deepens reasoning for either qualification tier.
Recall & Review
Retrieval without notes
Six retrieval points. Enter a number, decimal, fraction such as 3/2, or mixed number such as 1 1/2. Equivalent numeric values are accepted. Unsupported notation goes to teacher review. For rounding, also communicate the requested accuracy in written work; numerical scoring cannot judge significant trailing zeros.
Not checked.
Independent exit evidence
P1–P2: five minutes, no notes, 4 marks. Your teacher reviews working and explanations. Full assessment solutions are not embedded.
Recall & Review and prepare
Coordinates record horizontal then vertical displacement. A translation moves every point by the same vector. Reflection preserves perpendicular distance to its mirror line.
Retrieve F1 again in one week. Bring your working and one question.
Your progress summary
Completion records attempts, not mastery. Retrieval points describe the latest checked attempt. Your teacher reviews P1–P2 separately and checks retained understanding after a delay.
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Optional extension activities
Allow 10–15 minutes if the main practice is secure. Show your method, explain a check and justify your conclusion.
Stretch
Reveal a worked check after attempting
4 cm; every point on the bisector is equidistant from endpoints.
Deep challenge
Reveal a worked check after attempting
Intersections of circles centred A radius 3 cm and B radius 4 cm, if the circles meet; up to two points.