O Level / IGCSE Mathematics chapter 3: Coordinate geometry MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

56 exam-style questions on Coordinate geometry, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

56 questions · 7 topics · 10 per test

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What chapter 3 covers

Ten Coordinate geometry questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. Three vertices of a rectangle are (1, 2), (5, 2) and (5, 6). What are the coordinates of the fourth vertex?

  1. A
    (6, 1)
  2. B
    (1, −2)
  3. C
    (5, 1)
  4. D
    (1, 6)
Show answer

Answer: D. The fourth vertex is directly above (1, 2) and level with (5, 6), so it is (1, 6). x-coordinate first, then y.

2. Find the equation of the line parallel to y = x/2 + 3 that passes through (4, −1).

  1. A
    y = x/2 + 1
  2. B
    y = −2x + 7
  3. C
    y = x/2 − 1
  4. D
    y = x/2 − 3
Show answer

Answer: D. Same gradient 1/2, so y = x/2 + c. Substitute (4, −1): −1 = 2 + c, so c = −3. Equation y = x/2 − 3.

3. A is (0, 2) and B is (4, 4). Find the length of AB, correct to 3 significant figures.

  1. A
    6
  2. B
    20
  3. C
    3.46
  4. D
    4.47
Show answer

Answer: D. Length = √(42 + 22) = √20 = 4.472… ≈ 4.47. Subtracting the squares (√(16 − 4) = 3.46) is Pythagoras used the wrong way.

4. The lines y = 2x + 1 and y = 7 − x are drawn on the same grid. At which point do they cross?

  1. A
    (5, 2)
  2. B
    (2, 5)
  3. C
    (3, 4)
  4. D
    (−2, 9)
Show answer

Answer: B. At the crossing point the y values are equal: 2x + 1 = 7 − x, so 3x = 6 and x = 2. Then y = 2 × 2 + 1 = 5, giving (2, 5).

5. ABCD is a parallelogram with A(0, 0), B(5, 0) and C(7, 3), labelled in order. Find the coordinates of D.

  1. A
    (−2, 3)
  2. B
    (5, 3)
  3. C
    (12, 3)
  4. D
    (2, 3)
Show answer

Answer: D. In a parallelogram AD is equal and parallel to BC. From B to C is 2 right and 3 up, so from A(0, 0) go 2 right and 3 up to D(2, 3).

6. The line through (−2, k) and (3, 7) has gradient 3. Find k.

  1. A
    8
  2. B
    22
  3. C
    2
  4. D
    −8
Show answer

Answer: D. (7 − k)/(3 − (−2)) = 3, so (7 − k)/5 = 3, 7 − k = 15 and k = −8. Check: from (−2, −8) to (3, 7) is up 15 across 5, gradient 3.

7. Find the length of the line joining (−2, 3) and (3, −9).

  1. A
    17
  2. B
    13
  3. C
    √37
  4. D
    169
Show answer

Answer: B. The horizontal difference is 5 and the vertical difference is 12, so length = √(52 + 122) = √169 = 13. Adding 5 + 12 gives 17.

8. A line has gradient 1/2 and y-intercept −3. Which is its equation?

  1. A
    x − 2y = −6
  2. B
    x + 2y = 6
  3. C
    x − 2y = 6
  4. D
    2x − y = 3
Show answer

Answer: C. y = x/2 − 3. Multiply by 2: 2y = x − 6, which rearranges to x − 2y = 6. Check: when x = 0, y = −3.

9. A rectangle has vertices (−2, −1), (4, −1), (4, 3) and (−2, 3). Find its area.

  1. A
    20 square units
  2. B
    4 square units
  3. C
    12 square units
  4. D
    24 square units
Show answer

Answer: D. Width = 4 − (−2) = 6 and height = 3 − (−1) = 4, so area = 6 × 4 = 24. Ignoring the negative signs gives 2 × 2 = 4, and 20 is the perimeter.

10. Where does the line y = 4x − 8 cross the y-axis?

  1. A
    (2, 0)
  2. B
    (0, 4)
  3. C
    (−8, 0)
  4. D
    (0, −8)
Show answer

Answer: D. On the y-axis x = 0, so y = −8 and the point is (0, −8). (2, 0) is where it crosses the x-axis.

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Ways to practise this chapter

Coordinate geometry: questions students ask

How many Coordinate geometry MCQs are there?

56, each with the answer and a short explanation, across 7 topics: Coordinates, Drawing linear graphs, Gradient of linear graphs, Length and midpoint, Equations of linear graphs, Parallel lines, Perpendicular lines. Every chapter test draws ten of them, so you can take it many times.

Is the O Level / IGCSE Mathematics chapter 3 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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