2 Points A and B are plotted on the grid. – 3 – 2 – 1 1 0 2 3 y x 4 3 2 1 – 1 – 2 – 3 A B (a) Write down the coordinates of point B. ( … , …) [1] (b) Write AB as a vector. f p [1] (c) On the grid, plot point C at (-2, 3). [1]

2(a) (2, 3) 1 2(b) 4 5    1 2(c) C plotted at (–2, 3) 1

19 x y 8 6 4 2 0 – 4 – 2 – 1 1 2 3 – 2 – 3 L Find the equation of line L. Give your answer in the form y mx c = + . y = … [3]

19 [y =] 3x + 2 final answer 3 B2 for [y =] 3x + c as answer or M1 for a correct rise/run e.g. 6 ÷ 2 or 8 2 2 0 − − or for a suitable right-angled triangle marked on graph with correct values shown for rise and run and B1 for [y =] mx + 2, m ≠ 0 as answer

21 (a) 5 4 3 2 1 0 – 1 – 1 6 5 4 3 2 1 – 2 – 3 – 4 – 2 x L y Find the equation of line L in the form y mx c = + . y = … [2] (b) Find the equation of the line which is • parallel to the line y x 3 5 = - and • passes through the point (0, 17). … [1]

21(a) −0.5x + 2 or – 1 2 x + 2 2 B1 for −0.5x + c oe or mx + 2 oe (m≠0) 21(b) y = 3x + 17 cao 1

9 A is the point (5, 5 - ) and B is the point (9, 3). (a) Find the coordinates of the midpoint of AB. ( …, … ) [2] (b) Find the length of AB. … [3]

9(a) (7, − 1) 2 B1 for each 9(b) 8.94 or 8.944… 3 M2 for ( ) ( ) 2 2 9 5 3 5 − + −− oe or M1 for ( ) ( ) 2 2 9 5 3 5 − + −− oe

11 Line L has equation y x 4 5 = - . Find the equation of a line that is perpendicular to line L and passes through the point (0, 6). … [3]

11 y = 1 6 5 + x oe final answer 3 B2 for y = 1 5 x + c oe or 1 5 x + 6 oe or y = mx + 6 oe or B1 for [gradient =] 1 5 oe or mx + 6

Cambridge IGCSE Mathematics · 0580

IGCSE Mathematics (0580) Coordinate geometry past paper questions

Coordinate geometry questions test gradients, straight-line equations, and the midpoint and length of a line. Practising them by topic fixes the y = mx + c method that later questions assume you already have.

124 free questions from 2016–2021, each with its marking scheme. Open the full topical bank to filter by subtopic, paper, and year.