Coordinate geometry — IGCSE Mathematics (0580) questions by topic
Coordinate geometry questions ask you to read a gradient directly from an equation such as y = 5x − 3, find the equation of a line drawn on a grid in the form y = mx + c, and draw a specified line on a grid alongside one already given. Find, draw, state, calculate and identify want the gradient and intercept correctly read off or calculated, not estimated by eye.
16 questions from 2023 to 2025 sit on this page, worth between 2 and 14 marks. Because reading a gradient or intercept from a badly drawn line is a common source of small errors, submitting your answer for instant marking flags a slightly-off gradient immediately, rather than that inaccuracy carrying through into every later calculation using the same line's equation.
May–June 2025, Paper 21
The line x + y = 7 is drawn on the grid. (The grid shows axes from 0 to 8 on the x-axis and 0 to 9 on the y-axis, with the line x + y = 7 drawn from (0, 7) to (7, 0).) On the…
Answer this question and get it marked →May–June 2025, Paper 23
A is the point (a, 12) and B is the point (b, 27). Find the y-coordinate of the midpoint of AB.
Answer this question and get it marked →May–June 2025, Paper 31
The equation of line L is y = 5x - 3. Write down the gradient of line L.
Answer this question and get it marked →Six sketch graphs labelled A to F are shown (not to scale), each on a set of x-y axes: - A: a horizontal line crossing the y-axis at y = 3. - B: a steep straight line through the…
Answer this question and get it marked →May–June 2025, Paper 32
The equation of a line is y = −5x + 7. Write down the gradient of this line.
Answer this question and get it marked →May–June 2025, Paper 42
P is the point (8, 0) and Q is the point (20, 6). Find the equation of the perpendicular bisector of PQ. Give your answer in the form y = mx + c.
Answer this question and get it marked →May–June 2025, Paper 43
Line L has the equation y = 2(x - 5). Find the coordinates of the point where line L intersects the y-axis.
Answer this question and get it marked →May–June 2023, Paper 22
C is the point (5, −1) and D is the point (13, 15). Find the midpoint of CD.
Answer this question and get it marked →May–June 2023, Paper 32
The diagram shows line L on a grid. Find the equation of line L. Give your answer in the form y = mx + c.
Answer this question and get it marked →May–June 2023, Paper 33
Write down the equation of line L in the form y = mx + c (L passes through (0, 3) with a negative gradient).
Answer this question and get it marked →May–June 2023, Paper 41
In square ABCD, A = (−2, 1) and B = (1, 5). C = (a, b) where a and b are both positive integers. Find the coordinates of C and the coordinates of D.
Answer this question and get it marked →May–June 2023, Paper 43
M has coordinates (4, 1) and N has coordinates (−2, −7). Find the length of MN.
Answer this question and get it marked →October–November 2023, Paper 12
Point A and line L are shown on the grid. Point A is plotted below the x-axis at (1, −2), and line L is a straight line drawn on the grid. Write down the coordinates of point A.
Answer this question and get it marked →October–November 2023, Paper 13
Line L is drawn on the grid. Find the equation of line L in the form y = mx + c.
Answer this question and get it marked →October–November 2023, Paper 31
Line L is drawn on the grid. Find the equation of line L in the form y = mx + c.
Answer this question and get it marked →October–November 2023, Paper 43
A is the point (0, 2), B is the point (3, 3) and C is the point (4, 0). Determine if triangle ABC is scalene, isosceles or equilateral. You must show all your working.
Answer this question and get it marked →Other IGCSE Mathematics topics
- Number (230)
- Algebra and graphs (150)
- Geometry (93)
- Mensuration (54)
- Statistics (52)
- Trigonometry (33)
- Transformations and vectors (32)
- Probability (27)