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Cambridge IGCSE Maths (0580) · Topic 3: Coordinate geometry · 3.1, 3.2

Cambridge IGCSE Maths 0580 Coordinates and Linear Graphs Questions

Coordinates and Linear Graphs questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.

Practise coordinates and linear graphs →Coordinates and Linear Graphs notes

What the syllabus asks

Summarised in our own words: check the exact wording in the official 0580 syllabus.

Coordinates and Linear Graphs questions: Core

For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).

Question 1 Core non-calculator · easy

\(A\) is \((2, 5)\), \(B\) is \((2, -1)\) and \(C\) is \((-3, -1)\).
Find the coordinates of \(D\) so that \(ABCD\) is a rectangle.

Show the worked answer
  1. \(AB\) is vertical (same \(x\)) and \(BC\) is horizontal (same \(y\)).
  2. \(D\) has the \(x\)-coordinate of \(C\) and the \(y\)-coordinate of \(A\).

Answer: \(D(-3, 5)\)

Question 2 Core non-calculator · easy

Complete the table of values for \(y = 3x - 2\).

x−10123
y
Show the worked answer
  1. \(x = -1\): \(-3 - 2 = -5\). \(x = 0\): \(-2\). \(x = 1\): \(1\). \(x = 2\): \(4\). \(x = 3\): \(7\).

Answer: \(-5, -2, 1, 4, 7\)

Question 3 Core calculator · easy · 2 marks

The points \((-2, 3)\) and \((4, 3)\) are plotted.

(a) Write down the equation of the line through both points.

(b) How far apart are the two points?

Show the answer and mark scheme
  • B1 (a) y = 3
  • B1 (b) 6 units

Answer: (a) \(y = 3\) (b) \(6\) units

Question 4 Core calculator · easy · 2 marks

The line \(y = 3x - 6\) is drawn. Write down the coordinates of the points where it crosses

(a) the \(y\)-axis (b) the \(x\)-axis.

Show the answer and mark scheme
  • B1 (a) (0, −6)
  • B1 (b) (2, 0)

Answer: (a) \((0, -6)\) (b) \((2, 0)\)

Question 5 Core non-calculator · medium

Does the point \((4, 9)\) lie on the line \(y = 2x + 1\)? Does the point \((-2, -5)\)? Show how you decide.

Show the worked answer
  1. \(x = 4\): \(2 \times 4 + 1 = 9\), which matches, so \((4, 9)\) is on the line.
  2. \(x = -2\): \(2 \times (-2) + 1 = -3\), not \(-5\), so \((-2, -5)\) is not on the line.

Answer: \((4, 9)\) yes; \((-2, -5)\) no

Question 6 Core non-calculator · medium

Find the coordinates of the points where the line \(2x + 3y = 12\) crosses the \(x\)-axis and the \(y\)-axis.

Show the worked answer
  1. On the \(x\)-axis \(y = 0\): \(2x = 12\), \(x = 6\).
  2. On the \(y\)-axis \(x = 0\): \(3y = 12\), \(y = 4\).

Answer: \((6, 0)\) and \((0, 4)\)

Question 7 Core non-calculator · medium

The lines \(y = x + 1\) and \(y = 7 - x\) are drawn on the same grid.
Find the coordinates of the point where they cross.

Show the worked answer
  1. At the crossing point both \(y\) values are equal: \(x + 1 = 7 - x\).
  2. \(2x = 6\), so \(x = 3\) and \(y = 4\).

Answer: \((3, 4)\)

Question 8 Core non-calculator · medium · 2 marks

\(A\) is \((-3, 2)\), \(B\) is \((1, 2)\) and \(C\) is \((1, -4)\). \(ABCD\) is a rectangle. Find the coordinates of \(D\).

Show the answer and mark scheme
  • B2 (−3, −4) (B1 for one coordinate correct)

Answer: \((-3, -4)\)

Question 9 Core non-calculator · hard

\(A(1, 1)\) and \(B(5, 1)\) are two corners of a square \(ABCD\). \(C\) and \(D\) are above the line \(AB\).
Find the coordinates of \(C\) and \(D\).

Show the worked answer
  1. \(AB = 5 - 1 = 4\) units, so each side is \(4\) units.
  2. \(C\) is \(4\) units above \(B\): \((5, 5)\). \(D\) is \(4\) units above \(A\): \((1, 5)\).

Answer: \(C(5, 5)\) and \(D(1, 5)\)

Examiner Insights: common mistakes in IGCSE Maths 0580, with fixes (our analysis of public sources) →

Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).

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Questions students ask

Which Cambridge 0580 papers can test coordinates and linear graphs?

Coordinates and Linear Graphs is on both tiers (syllabus 3.1, 3.2), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.

Are these Cambridge past-paper questions?

No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.

Where can I practise more coordinates and linear graphs questions?

In the 0580 practice for topic 3 (Coordinate geometry), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.

More coordinate geometry questions