[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207795-en":3,"doc-seo-207795-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},207795,2336477552062,"Stanford","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",4,"Exam","Equations of a Line - CIE IGCSE Maths 0580 Extended Theory Question Paper 3","Equations of a Line - Question Paper 3 focuses on coordinate geometry and core line skills for Cambridge IGCSE Maths (0580). The questions cover finding mid-points, gradients and intercept form, determining unknown parameters from parallel lines, and writing equations of lines through given points. Additional tasks include calculating distances between coordinates, constructing the perpendicular bisector using straight edge and compasses, and solving systems to locate intersection points and mid-points.","Equations of a Line (gradients, mid-points, perpendicular & parallel lines)  \nQuestion Paper 3  \n\n| Level | IGCSE |\n| --- | --- |\n| Subject | \u003Cbr>Maths (0580) |\n| Exam Board | Cambridge International Examinations (CIE) |\n| Paper Type | \u003Cbr>Extended |\n| Topic | Co-ordinate geometry |\n| Sub-Topic | \u003Cbr>Equations ofa Line |\n| Booklet | Question Paper 3 |\n| Time Allowed:\u003Cbr>Score:\u003Cbr>Percentage:\u003Cbr>Grade Boundaries: | 62 minutes /51 / 100 |\n| A* A | B C D E U |\n| >85% 75% | 60% 45% 35% 25% \u003C25% |\n\n1 (a) Find the co-ordinates of the midpoint of the line joining A(–8, 3) and B(–2,–3) .  \nAnswer(a) (  ,  ) [2]  \n(b) The line y = 4x + c passes through (2, 6) .  \nFind the value ofc.  \nAnswer(b) c =   [1]  \n(c) The lines 5x = 4y + 10 and 2y = kx – 4 are parallel.  \nFind the value ofk.  \nAnswer(c) k =   [2]  \n2  \ny  \nO  \nNOT TO SCALE  \nThe co-ordinates ofA, B and C are shown on the diagram, which is not to scale.  \n(a) Find the length of the line AB.  \nAnswer(a) AB =   [3]  \n(b) Find the equation of the line AC.  \nAnswer(b)   [3]  \n3 Find the length of the straight line from Q (−8, 1) to R (4 , 6) .  \nAnswer QR =   [3]  \n4  \ny  \n4  \n3  \n2  \n1  \n1 2  \nx  \nThe lines AB and CB intersect at B.  \n(a) Find the co-ordinates of the midpoint of AB.  \nAnswer(a) (  ,  ) [1]  \n(b) Find the equation of the line CB.  \nAnswer(b)   [3]  \n5  \nNOT TO SCALE  \nx  \nThe diagram shows the straight line which passes through the points (0, 1) and (3, 13) .  \nFind the equation of the straight line.  \nAnswer   [3]  \n6  \ny  \n8  \n7  \n6  \n5  \n4  \n3  \n2  \n1  \n0  \n–1  \n–2  \n–3  \n–4  \nA  \n1 2  \nx  \nB  \n(a) Using a straight edge and compasses only, construct the perpendicular bisector of AB on the diagram above. [2]  \n(b) Write down the co-ordinates of the midpoint of the line segment joining A(1, 8) to B(7,–4) .  \nAnswer(b) (  ,  ) [1]  \n(c) Find the equation of the line AB.  \nAnswer(c)   [3]  \n7 (a) The line y = 2x + 7 meets they-axis at A.  \nWrite down the co-ordinates ofA.  \nAnswer(a) A = (  ,  ) [1]  \n(b) A line parallel toy = 2x + 7 passes through B(0, 3) .  \n(i) Find the equation of this line.  \nAnswer(b)(i)   [2]  \n(ii) C is the point on the line y = 2x + 1 where x = 2.  \nFind the co-ordinates of the midpoint of BC.  \nAnswer(b)(ii) (  ,  ) [3]  \n8 Find the equation of the straight line which passes through the points (0, 8) and (3, 2) .  \nAnswer   [3]  \n9 The points (2, 5),(3, 3) and (k, 1) all lie in a straight line.  \n(a) Find the value ofk.  \nAnswer(a) k =   [1]  \n(b) Find the equation of the line.  \nAnswer(b)   [3]  \n10  \n\n| 4 | A |  | NOT TO SCALE\u003Cbr>y = 4 |\n| --- | --- | --- | --- |\n|  |  | B |  |\n| 0 |  |  |  |\n\ny  \n2x + y = 8 3x + y = 18  \n x  \n(a) The line y = 4 meets the line 2x + y = 8 at the point A.  \nFind the co-ordinates ofA.  \nAnswer(a) A (  ,  ) [1]  \n(b) The line 3x + y = 18 meets the x axis at the point B.  \nFind the co-ordinates of B.  \nAnswer(b) B (  ,  ) [1]  \n(c) (i) Find the co-ordinates of the mid-point M of the line joining A to B.  \nAnswer(c)(i) M (  ,  ) [1]  \n(ii) Find the equation of the line through M parallel to 3x + y = 18.  \nAnswer(c)(ii)   [2]  \n11 Find the length of the line joining the points A(−4, 8) and B(−1, 4) .  \nAnswer AB =   [2]","cbCaip1xKlcbNF4L","https://ap.wps.com/l/cbCaip1xKlcbNF4L","pdf",805661,1,11,"English","en",105,"# Equations of a Line\n## Mid-points and lengths\n## Line equations, gradients, and parallels\n## Perpendicular bisector construction","[{\"question\":\"What topics are tested in Equations of a Line Question Paper 3?\",\"answer\":\"It tests coordinate geometry skills such as mid-points, lengths between points, gradients, and writing equations of lines. It also includes conditions for parallel lines and a perpendicular bisector construction.\"},{\"question\":\"How do students find midpoints in these questions?\",\"answer\":\"Students determine the midpoint coordinates of a line segment using the given endpoint coordinates, then write the midpoint as a coordinate pair.\"},{\"question\":\"What types of line equation questions appear?\",\"answer\":\"The paper asks for line equations from points (e.g., two given coordinates), from a given line with an unknown constant, and from relationships like parallel lines. It also uses systems to find intersection points.\"}]","Equations of a Line - CIE IGCSE Maths 0580 Extended Theory Question Paper 3 | PDF",1788601164,28,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"equations-of-a-line-cie-igcse-maths-0580-extended-theory-question-paper-3","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/exam/",3,{"item":52,"name":13,"@type":43,"position":11},"https://docshare.wps.com/document/equations-of-a-line-cie-igcse-maths-0580-extended-theory-question-paper-3/207795/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-09-06","2026-09-05",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What topics are tested in Equations of a Line Question Paper 3?","Question",{"text":75,"@type":76},"It tests coordinate geometry skills such as mid-points, lengths between points, gradients, and writing equations of lines. 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