Equations of a Line - CIE IGCSE Maths 0580 Extended Theory Question Paper 3

Q: What topics are tested in Equations of a Line Question Paper 3?

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.

Q: How do students find midpoints in these questions?

Students determine the midpoint coordinates of a line segment using the given endpoint coordinates, then write the midpoint as a coordinate pair.

Q: What types of line equation questions appear?

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.

Sep 5, 2026

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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.

LanguageEnglish

CategoryExam

FormatPDF

Pages11

Reading Time28 min

AccessFree to download

Equations of a Line

Mid-points and lengths

Line equations, gradients, and parallels

Perpendicular bisector construction

Equations of a Line (gradients, mid-points, perpendicular & parallel lines) Question Paper 3 | Level | IGCSE | | --- | --- | | Subject |
Maths (0580) | | Exam Board | Cambridge International Examinations (CIE) | | Paper Type |
Extended | | Topic | Co-ordinate geometry | | Sub-Topic |
Equations ofa Line | | Booklet | Question Paper 3 | | Time Allowed:
Score:
Percentage:
Grade Boundaries: | 62 minutes /51 / 100 | | A* A | B C D E U | | >85% 75% | 60% 45% 35% 25% <25% | 1 (a) Find the co-ordinates of the midpoint of the line joining A(–8, 3) and B(–2,–3) . Answer(a) ( , ) [2] (b) The line y = 4x + c passes through (2, 6) . Find the value ofc. Answer(b) c = [1] (c) The lines 5x = 4y + 10 and 2y = kx – 4 are parallel. Find the value ofk. Answer(c) k = [2] 2 y O NOT TO SCALE The co-ordinates ofA, B and C are shown on the diagram, which is not to scale. (a) Find the length of the line AB. Answer(a) AB = [3] (b) Find the equation of the line AC. Answer(b) [3] 3 Find the length of the straight line from Q (−8, 1) to R (4 , 6) . Answer QR = [3] 4 y 4 3 2 1 1 2 x The lines AB and CB intersect at B. (a) Find the co-ordinates of the midpoint of AB. Answer(a) ( , ) [1] (b) Find the equation of the line CB. Answer(b) [3] 5 NOT TO SCALE x The diagram shows the straight line which passes through the points (0, 1) and (3, 13) . Find the equation of the straight line. Answer [3] 6 y 8 7 6 5 4 3 2 1 0 –1 –2 –3 –4 A 1 2 x B (a) Using a straight edge and compasses only, construct the perpendicular bisector of AB on the diagram above. [2] (b) Write down the co-ordinates of the midpoint of the line segment joining A(1, 8) to B(7,–4) . Answer(b) ( , ) [1] (c) Find the equation of the line AB. Answer(c) [3] 7 (a) The line y = 2x + 7 meets they-axis at A. Write down the co-ordinates ofA. Answer(a) A = ( , ) [1] (b) A line parallel toy = 2x + 7 passes through B(0, 3) . (i) Find the equation of this line. Answer(b)(i) [2] (ii) C is the point on the line y = 2x + 1 where x = 2. Find the co-ordinates of the midpoint of BC. Answer(b)(ii) ( , ) [3] 8 Find the equation of the straight line which passes through the points (0, 8) and (3, 2) . Answer [3] 9 The points (2, 5),(3, 3) and (k, 1) all lie in a straight line. (a) Find the value ofk. Answer(a) k = [1] (b) Find the equation of the line. Answer(b) [3] 10 | 4 | A | | NOT TO SCALE
y = 4 | | --- | --- | --- | --- | | | | B | | | 0 | | | | y 2x + y = 8 3x + y = 18 x (a) The line y = 4 meets the line 2x + y = 8 at the point A. Find the co-ordinates ofA. Answer(a) A ( , ) [1] (b) The line 3x + y = 18 meets the x axis at the point B. Find the co-ordinates of B. Answer(b) B ( , ) [1] (c) (i) Find the co-ordinates of the mid-point M of the line joining A to B. Answer(c)(i) M ( , ) [1] (ii) Find the equation of the line through M parallel to 3x + y = 18. Answer(c)(ii) [2] 11 Find the length of the line joining the points A(−4, 8) and B(−1, 4) . Answer AB = [2]

FAQs

What topics are tested in Equations of a Line Question Paper 3?

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.

How do students find midpoints in these questions?

Students determine the midpoint coordinates of a line segment using the given endpoint coordinates, then write the midpoint as a coordinate pair.

What types of line equation questions appear?

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.

Sep 5, 2026

Upload by Stanford