Leaving Cert Maths: Coordinate geometry: line
How often Coordinate geometry: line comes up on the Maths papers, every year it was asked, and questions to try.
HL Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
OL Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker
FL Asked on 3 of the last 7 Foundation Level papers, most recently in 2025.
Quick ones on Coordinate geometry: line.
- 1/3
- 3
- 6
- 2
- 5
- −2
- −1
- 0
- 1
Show the answers
(a) 3
(b) −2
(c) −1
Higher Level
Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q4 |
| 2025 | Q1 |
| 2024 | Q6, Q9 |
| 2023 | Q3 |
| 2022 | Q2 |
| 2021 | Q2 |
| 2019 | Q2 |
| 2018 | Q5 |
| 2017 | Q3 |
| 2016 | Q1, Q2 |
Links open the State Examinations Commission’s paper for that year.
More Coordinate geometry: line questions
Coordinate geometry: line, 2 marks
Slope of the line 2x + 3y − 6 = 0?
- 2/3
- −3/2
- −2/3
Show the answer
−2/3
Rearrange to y = mx + c: 3y = −2x + 6, so y = −(2/3)x + 2. Shortcut: slope = −a/b.
Coordinate geometry: line, 2 marks
Perpendicular distance from (x₁, y₁) to ax + by + c = 0?
- |ax₁ + by₁| / √(a² + b²)
- |ax₁ + by₁ + c| / √(a² + b²)
- (ax₁ + by₁ + c) / (a² + b²)
Show the answer
|ax₁ + by₁ + c| / √(a² + b²)
Substitute the point into the line's equation, take the absolute value, and divide by √(a² + b²). It's in the tables.
Coordinate geometry: line, 2 marks
Where does y = 2x − 8 cross the x-axis?
- (4, 0)
- (−8, 0)
- (−4, 0)
Show the answer
(4, 0)
On the x-axis y = 0: 2x − 8 = 0, so x = 4.
Ordinary Level
Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q1, Q7 |
| 2025 | Q4 |
| 2024 | Q3 |
| 2023 | Q1 |
| 2022 | Q1 |
| 2021 | Q3, Q10 |
| 2019 | Q2, Q4 |
| 2018 | Q2, Q4 |
| 2017 | Q3, Q8 |
| 2016 | Q4, Q9 |
Links open the State Examinations Commission’s paper for that year.
More Coordinate geometry: line questions
Coordinate geometry: line, 2 marks
Find the slope of the line through (2, 1) and (6, 9).
- 1/2
- 8
- 2
Show the answer
2
m = (y₂ − y₁)/(x₂ − x₁) = (9 − 1)/(6 − 2) = 8/4 = 2.
Coordinate geometry: line, 2 marks
What is the slope of y = 3x − 7?
- 7
- 3
- −7
Show the answer
3
In the form y = mx + c the slope is m, the number in front of x. Here m = 3.
Coordinate geometry: line, 2 marks
Find the midpoint of (2, 4) and (6, 10).
- (4, 7)
- (8, 14)
- (2, 3)
Show the answer
(4, 7)
Midpoint = ((2 + 6)/2, (4 + 10)/2) = (4, 7). Add the coordinates, then halve.
Foundation Level
Asked on 3 of the last 7 Foundation Level papers, most recently in 2025.
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Not asked |
| 2025 | Q8 |
| 2024 | Q6 |
| 2023 | Q6 |
| 2022 | Not asked |
| 2021 | Not asked |
| 2019 | Not asked |
Links open the State Examinations Commission’s paper for that year.
More Coordinate geometry: line questions
Coordinate geometry: line, 2 marks
Start at the origin. Go 3 units right and 2 units up. What are the coordinates of this point?
- (2, 3)
- (3, −2)
- (3, 2)
Show the answer
(3, 2)
Coordinates are written (across, up). 3 across and 2 up is (3, 2).
Coordinate geometry: line, 2 marks
Point A is (−2, 3). What is its image under axial symmetry in the x-axis?
- (2, −3)
- (−2, −3)
- (2, 3)
Show the answer
(−2, −3)
Reflecting in the x-axis keeps the x value and changes the sign of the y value: (−2, −3).
Coordinate geometry: line, 2 marks
Which of these points lies on the y-axis?
- (0, 5)
- (5, 0)
- (5, 5)
Show the answer
(0, 5)
Points on the y-axis have x = 0, so (0, 5) is on it.