rder":3,"title":"Draw arcs from $K$","content":"**Without changing the width of your compass**, move the needle to point $K$.\n\nDraw another two arcs:\n- One arc above the line segment $JK$ that intersects the first arc.\n- One arc below the line segment $JK$ that intersects the first arc.\n\nYou should now have two distinct intersection points (crosses) made by the arcs.\n\n*(This earns the first method mark M1 for creating two pairs of intersecting arcs of equal radius from $J$ and $K$.)*"},{"type":"text","order":4,"title":"Draw the perpendicular line","content":"Using a ruler, draw a single straight line that passes directly through the two intersection points of your arcs.\n\nThis line is the perpendicular bisector of $JK$. Leave all your construction arc lines visible on the page to show your working.\n\n*(This earns the final accuracy mark A1 for the correctly drawn perpendicular line.)*"}]}],"generatedAt":"2026-06-12T13:04:50.239Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null},{"id":"8c6f3735-9437-4dc5-b7ad-9d8d23e33b9a","revisionId":"33af2e60-e645-47f5-8492-cf98a52f9408","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"2f1ea0ad-e07c-4422-93a1-3cf99ea08748","label":"a","content":"In the space below, use a ruler and compasses to construct an equilateral triangle where each side is $4.5\\text{ cm}$ long.\n\nYou must show all your construction lines.","markscheme":"- Base line of $4.5\\text{ cm}$ accurately drawn. B1\n- Two intersecting arcs with radius $4.5\\text{ cm}$ drawn from endpoints. M1\n- Triangle correctly completed. A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Draw base line of $4.5\\text{ cm}$ length.","code":"B"},{"id":"p2","marks":1,"description":"Compass arcs of radius $4.5\\text{ cm}$ shown intersecting above or below the base line.","code":"M"},{"id":"p3","marks":1,"description":"Final triangle drawn with straight edges connecting to arc intersection.","code":"A"}],"finalAnswers":["Equilateral triangle with side 4.5 cm"],"generatedAt":"2026-05-06T14:02:57.612Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"ruler_and_compasses","label":"Ruler and compasses construction","steps":[{"type":"drawing","order":1,"title":"Draw the base","width":600,"height":448,"shapes":[{"id":"base","type":"line","color":"blue","points":[{"x":120,"y":380},{"x":480,"y":380}]},{"x":97,"y":396,"id":"label_a","size":"m","text":"A","type":"text"},{"x":262,"y":396,"id":"length","size":"m","text":"4.5 cm","type":"text"},{"x":490,"y":396,"id":"label_b","size":"m","text":"B","type":"text"}],"caption":"Using a ruler and a sharp pencil, draw the base line $AB$ accurately so that it is $4.5\\text{ cm}$ long. This earns the B1 mark."},{"type":"drawing","order":2,"title":"Draw equal arcs","width":600,"height":448,"shapes":[{"id":"base","type":"line","color":"blue","points":[{"x":120,"y":380},{"x":480,"y":380}]},{"id":"arc_a","type":"plot","color":"grey","segments":[[{"x":56,"y":25.734562792247516},{"x":80,"y":22.22912360003363},{"x":120,"y":20},{"x":160,"y":22.22912360003363},{"x":200,"y":29.00142450431514},{"x":240,"y":40.588745030457176},{"x":280,"y":57.509690068058035},{"x":300,"y":68.23085463760208},{"x":340,"y":95.04386302449984},{"x":380,"y":131.00200804022535},{"x":420,"y":181.002512578676},{"x":459,"y":258.84307696214796}]]},{"id":"arc_b","type":"plot","color":"grey","segments":[[{"x":544,"y":25.734562792247516},{"x":520,"y":22.22912360003363},{"x":480,"y":20},{"x":440,"y":22.22912360003363},{"x":400,"y":29.00142450431514},{"x":360,"y":40.588745030457176},{"x":320,"y":57.509690068058035},{"x":300,"y":68.23085463760208},{"x":260,"y":95.04386302449984},{"x":220,"y":131.00200804022535},{"x":180,"y":181.002512578676},{"x":141,"y":258.84307696214796}]]},{"h":8,"w":8,"x":296,"y":64.23085463760208,"id":"int

Loci and Construction

Question 5

Loci and Construction Questions

Loci and Construction

Question 5

Loci and Construction Questions