Missing vertex · Core / Foundation
ABCD is a parallelogram with A(1, 1), B(5, 2) and C(6, 5). Find D.
- From B to A: 4 left, 1 down
- Do the same from C: (6 − 4, 5 − 1)
Answer: D(2, 4)
Quadrilaterals, area & symmetry on a grid
Coordinate Polygon Detective
Mapped to Cambridge IGCSE 0580 (C/E3.1 coordinates, C/E4.1 special quadrilaterals, C/E4.5 symmetry, C/E5.2 area, E3.6–3.7 gradients) and GCSE A8, A9, G4 and G16, with question types from recent papers: “find the coordinates of point D of the parallelogram”, “the triangle drawn using the lines y = x, x = −2 and y = 4”, “angle ABC is a right angle, find k”.
What students practise
- Missing vertex of a square, rectangle, parallelogram, rhombus or kite
- Naming quadrilaterals from evidence, not appearance
- Properties of the special quadrilaterals: sides, angles and diagonals
- Lines of symmetry and order of rotational symmetry
- Area of triangles, parallelograms and trapeziums from coordinates; perimeters with Pythagoras
- Shapes enclosed by straight lines: corners and areas
- Right angles and parallel sides from gradients (Higher / Extended)
- Classifying a quadrilateral from coordinates alone; diagonals that bisect each other (Higher / Extended)
How it works
Learn
10 lessons, each labelled with the exams it is for, with an interactive shape model and worked examples.
Practise
Five stations, six fresh questions each visit, with hints that fade.
Challenge
Mixed questions from every station with a skill-by-skill report.
For teachers
Open Teacher Options in the game to choose skills and levels. Nothing is uploaded: progress stays in each student's browser, so no accounts or data-protection paperwork are needed.
Which exams it covers
Every station is matched to the current specifications. Teacher options switch between Core/Foundation and Extended/Higher questions.
| Topic | GCSE (AQA, Edexcel) | Cambridge IGCSE 0580 |
|---|---|---|
| Missing vertices and coordinates of shapes | A8, G4 | C3.1 / E3.1 |
| Special quadrilaterals: vocabulary and properties | G4 | C4.1 / E4.1 |
| Line and rotational symmetry of quadrilaterals | G4 | C4.5 / E4.5 |
| Area and perimeter of triangles, parallelograms and trapeziums | G16, G20 | C5.2 / E5.2 |
| Shapes enclosed by straight lines | A8, A9 | C3.2 / E3.2, E3.5 |
| Parallel and perpendicular sides from gradients | A9 (Higher) | E3.6, E3.7 (Extended) |
Worked examples
Four examples of the question types in the game.
Area · Core / Foundation
Find the area of the triangle with vertices (1, 1), (7, 1) and (4, 6).
- The base is horizontal: 7 − 1 = 6
- The perpendicular height is 6 − 1 = 5
- Area = ½ × 6 × 5
Answer: 15 square units
Shapes from lines · Higher
A triangle is drawn using the lines y = x, x = −2 and y = 4. Work out the coordinates of its vertices.
- y = x and x = −2 meet at (−2, −2)
- x = −2 and y = 4 meet at (−2, 4)
- y = x and y = 4 meet at (4, 4)
Answer: (−2, −2), (−2, 4), (4, 4)
Gradient check · Extended / Higher
A(1, 2), B(4, 6), C(8, 3). Is angle ABC a right angle?
- Gradient AB = 4 ÷ 3 = 4/3
- Gradient BC = −3 ÷ 4 = −3/4
- 4/3 × (−3/4) = −1
Answer: yes, AB is perpendicular to BC
Common mistakes the game targets
- Joining vertices in the wrong order. ABCD means A to B to C to D and back to A. AC and BD are diagonals, not sides.
- Trusting the diagram. A tilted square may really be a rhombus. Check the sides and the angles.
- Using the sloping side as the height. Areas need the perpendicular height.
- Counting the diagonals of a rectangle as lines of symmetry. A rectangle has 2 lines of symmetry, through the midpoints of opposite sides.
- Using the wrong perpendicular test. Perpendicular gradients multiply to −1; parallel gradients are equal.
Questions teachers and parents ask
Is the game free?
Yes. It is free to use, with no account, no adverts and no tracking.
Which exams does it suit?
Cambridge IGCSE 0580 Core and Extended, and GCSE Foundation and Higher (AQA and Edexcel). The gradient checks are Extended / Higher only. Every lesson shows which exam and tier it is for.
Does it include the shoelace formula or coordinate proof?
No. Neither is on the IGCSE or GCSE syllabus, so the game sticks to the methods the mark schemes expect: base × height, the rectangle-around-the-triangle method, Pythagoras and gradients.
Which words does it use for shapes?
UK and Cambridge terms: trapezium (exactly one pair of parallel sides), rhombus, kite and parallelogram.
How does scoring work?
2 points for a correct first attempt, 1 for a second attempt. A station is mastered at 80%.
Need worksheets and lessons to go with the games?
Printable IGCSE and GCSE resources from Mathwright: worksheets, exam-style practice and full worked solutions.
More coordinate geometry games
Coordinates & the four quadrants
Coordinate Treasure Map
Travel from Base Camp to the Treasure Chest by reading, plotting and moving between coordinates in all four quadrants.
Midpoint & length of a line segment
Coordinate Rescue Mission
Six stations on the midpoint and length of a line segment, missing points, exact surd lengths and dividing a line, with past-paper question types.
Gradient & straight-line graphs
Gradient City
Six stations covering every straight-line question on IGCSE and GCSE papers: gradient, drawing graphs, y = mx + c, parallel and perpendicular lines, and real-life gradients.