AQA GCSE Mathematics Paper 3 (Foundation), June 2025: Question 2

2 marks · Easy difficulty · Short Answer

Find the coordinates of point B on a coordinate grid and determine the coordinates of the midpoint of the line AB.

Practise this question

Question

A Cartesian grid with x-axis from 0 to 9 and y-axis from 0 to 7. A vertical straight line segment AB is drawn with point A at (8, 7) and point B at (8, 1). Part (a) asks to write down the coordinates of B, and part (b) asks to write down the coordinates of the midpoint of the line AB.

Mark scheme

Show the mark scheme Mark scheme table for question 2. For 2(a), the answer is (8, 1) awarded 1 mark (B1) with note 'Check the diagram if answer line is blank'. For 2(b), the answer is (8, 4) awarded 1 mark (B1) with a special case note: SC1 for (1, 8) in (a) and (4, 8) in (b).

How to answer it

Reading Coordinates & Finding Midpoints

📋 Revision Summary

What this question tests

This question assesses your foundational coordinate geometry skills on a Cartesian grid:

  • Accurately reading the (x, y) coordinates of a given point on a 1 cm grid.
  • Finding the midpoint of a vertical line segment either by visual counting or by using the midpoint formula: ((x₁ + x₂)/2, (y₁ + y₂)/2) .
  • Remembering the correct order of coordinates: along the corridor (x), then up the stairs (y).
Part (a)

Coordinates of Point B

Question: Write down the coordinates of B. [1 mark]

✅ Correct Answer

(8, 1)

Mark Scheme: 1 mark (B1) for the correct coordinate pair.

💡 Key Knowledge

  • Coordinates are always written in parentheses separated by a comma: (x, y) .
  • x-coordinate comes first: read straight down to the horizontal axis.
  • y-coordinate comes second: read straight across to the vertical axis.

🧠 Exam Technique

Find point B at the bottom end of the line segment:

  1. Look directly down to the horizontal axis: it lines up with 8.
  2. Look directly across to the vertical axis: it lines up with 1.
  3. Combine them inside brackets: (8, 1).

❌ Common Errors

  • Swapping the axes: Writing (1, 8) instead of (8, 1) .
  • Missing brackets: Writing 8, 1 without brackets (always use proper coordinate form).
  • Reading point A instead: Point A is at the top at (8, 7) . Double-check which label you are asked for!
Part (b)

Coordinates of the Midpoint of Line AB

Question: Write down the coordinates of the midpoint of the line AB. [1 mark]

✅ Correct Answer

(8, 4)

Mark Scheme: 1 mark (B1).
Special Case (SC1): Awarded for (1, 8) in part (a) and (4, 8) in part (b) if coordinates were consistently reversed.

📐 Calculations (Step-by-Step)

Method 1: Using the Midpoint Formula

  1. Identify endpoints:
    A = (8, 7) and B = (8, 1)
  2. Calculate midpoint x:
    (8 + 8) ÷ 2 = 16 ÷ 2 = 8
  3. Calculate midpoint y:
    (7 + 1) ÷ 2 = 8 ÷ 2 = 4
  4. Combine coordinates:
    (8, 4)

Method 2: Visual Grid Inspection

  1. Total length of vertical segment = 7 − 1 = 6 units.
  2. Halfway distance = 6 ÷ 2 = 3 units.
  3. Count 3 units up from B: 1 + 3 = 4.
  4. The line is vertical along x = 8, so the midpoint is (8, 4).

🧠 Examiner Insight

Examiners noted that many candidates lost full marks simply by reversing the coordinates to (4, 8) . The mark scheme includes a special case (SC1) that rewards a candidate 1 mark overall if they swapped x and y consistently across both parts (a) and (b), but avoiding this mistake guarantees the full 2 marks!

❌ Common Errors

  • Reversing coordinates: Writing (4, 8) by confusing the x- and y-values.
  • Giving length instead of position: Writing just 3 or 4 instead of a coordinate pair with brackets.
  • Midpoint arithmetic slip: Subtracting instead of adding: (7 − 1) ÷ 2 = 3 , then incorrectly writing (8, 3) .

Topics

Algebra · Geometry and measures · 3.2.2 Graphs · 3.4.1 Properties and constructions

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 3 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.