Plot and read coordinates in all four quadrants, find lengths and midpoints, and complete shapes on a grid. It is a Foundation topic, aimed at grade 1. Free questions with answers are on this page. Worked examples show each line before you try the questions.
A coordinate pair (x,y) is an instruction: x steps across from the origin, then y steps up (or down if y is negative). The x-axis is horizontal; the y-axis is vertical. Every point on the y-axis has x=0, so (0,−4) sits on the y-axis four units down.
The midpoint of two points is the average of the xs and the average of the ys. From (0,0) to (6,8) the midpoint is (3,4). A vertical line has equal x-coordinates; its length is just the difference in y. A horizontal line is the difference in x.
Read coordinates in the right order. (1,3) is not the same as (3,1). Plotting (3,1) when the question said (1,3) is a one-mark disaster that then wrecks a midpoint or length.
Objectives
Read an ordered pair as (x, y).
Move a point right or up and write the new coordinates.
Tell the x-axis from the y-axis.
Key points
Read and plot points such as (3, −2) in any of the four quadrants.
Find the length of a horizontal or vertical line from its end coordinates.
Find the midpoint of a line segment.
Find the missing vertex of a square, rectangle or parallelogram.
Worked examples
Example 1
A point is at (2, 3). It moves 4 squares right. What are the new coordinates?
2 marks
Moving right changes only the x-coordinate.
x: 2 + 4 = 6.
The new point is (6, 3).
Answer: (6, 3)
Common slips
Slip: Moving right changes only the y-coordinate. Left and right run along the x-axis, so only x changes.
Slip: x: 2 − 4 = −2. Moving right adds to x.
Slip: The new point is (2, 7). The move was applied to y. A sideways move leaves y alone.
Example 2
A point is at (1, 2). It moves 4 squares left. What are the new coordinates?
2 marks
Moving left changes only the x-coordinate.
x: 1 − 4 = −3.
The new point is (−3, 2).
Answer: (−3, 2)
Common slips
Slip: Moving left changes only the y-coordinate. Left and right run along the x-axis, so only x changes.
Slip: x: 1 + 4 = 5. Moving left subtracts from x.
Slip: The new point is (1, −2). The move was applied to y. A sideways move leaves y alone.
Example 3
A point is at (−3, −2). It moves 5 squares right and 3 squares up. What are the new coordinates?
3 marks
x: −3 + 5 = 2.
y: −2 + 3 = 1.
The new point is (2, 1).
Answer: (2, 1)
Common slips
Slip: x: −3 − 5 = −8. Moving right adds to x.
Slip: y: −2 − 3 = −5. Moving up adds to y.
Slip: The new point is (1, 2). The coordinates are the wrong way round. The x-coordinate comes first.
Questions and answers
GCSE Maths coordinates questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
A point is at (1, 1). It moves 3 squares right. What are the new coordinates?
Show answer
Answer: (4, 1)
Moving right changes only the x-coordinate.
x: 1 + 3 = 4.
M1 — Moving right changes only the x-coordinate.
A1 — Answer (4, 1)
Question 2 Easy2 marks
A point is at (0, 2). It moves 4 squares up. What are the new coordinates?
Show answer
Answer: (0, 6)
Moving up changes only the y-coordinate.
y: 2 + 4 = 6.
M1 — Moving up changes only the y-coordinate.
A1 — Answer (0, 6)
Question 3 Medium2 marks
A point is at (−2, 3). It moves 5 squares right. What are the new coordinates?
Show answer
Answer: (3, 3)
Moving right changes only the x-coordinate.
x: −2 + 5 = 3.
M1 — Moving right changes only the x-coordinate.
A1 — Answer (3, 3)
Question 4 Medium2 marks
A point is at (2, −1). It moves 4 squares up. What are the new coordinates?
Show answer
Answer: (2, 3)
Moving up changes only the y-coordinate.
y: −1 + 4 = 3.
M1 — Moving up changes only the y-coordinate.
A1 — Answer (2, 3)
Question 5 Hard2 marks
A point is at (2, 1). It moves 3 squares right and 2 squares up. What are the new coordinates?
Show answer
Answer: (5, 3)
x: 2 + 3 = 5.
y: 1 + 2 = 3.
M1 — x: 2 + 3 = 5.
A1 — Answer (5, 3)
Question 6 Hard2 marks
A point is at (−1, 4). It moves 2 squares right and 6 squares down. What are the new coordinates?
Show answer
Answer: (1, −2)
x: −1 + 2 = 1.
y: 4 − 6 = −2.
M1 — x: −1 + 2 = 1.
A1 — Answer (1, −2)
Question 7 Exam-style3 marks
A point is at (−2, −3). It moves 6 squares right and 4 squares up. What are the new coordinates?
Show answer
Answer: (4, 1)
x: −2 + 6 = 4.
y: −3 + 4 = 1.
The new point is (4, 1).
M1 — x: −2 + 6 = 4.
M1 — y: −3 + 4 = 1.
A1 — Answer (4, 1)
Common mistakes
Most lost marks on this topic are one slip.
Writing y first.
The pair is always (x, y), across then up.
Adding the move to both coordinates.
A move right changes only x. A move up changes only y.
Counting the origin as 1.
The origin is 0 in both directions.
Spot the slip
On a grid, which direction is the x-coordinate?
Across
Up
Diagonal
Show the slip
Across x goes across. y goes up.
Exam tips
Be ready to do this without a calculator. Paper 1 is the non-calculator paper.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Plot points with a neat small cross, not a blob — a cross that is out by a square loses the mark.
Label every point you plot with its letter so the examiner can follow your working.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.