O Level / IGCSE Mathematics chapter 7: Transformations and vectors MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

27 exam-style questions on Transformations and vectors, 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.

27 questions · 3 topics · 10 per test

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What chapter 7 covers

Ten Transformations and vectors questions with answers

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

1. The point (5, 7) is enlarged by scale factor 1/2 with centre (1, 1). Find the image of the point.

  1. A
    (2.5, 3.5)
  2. B
    (4, 5)
  3. C
    (9, 13)
  4. D
    (3, 4)
Show answer

Answer: D. From the centre (1, 1) to (5, 7) is 4 across and 6 up. Halve these: 2 across and 3 up from the centre gives (3, 4). Halving the coordinates themselves only works when the centre is the origin.

2. a = (6, −3), written as a column vector. Find the column vector c such that 2c + a = (0, 7).

  1. A
    (−3, 2)
  2. B
    (−6, 10)
  3. C
    (−3, 5)
  4. D
    (3, 2)
Show answer

Answer: C. 2c = (0, 7) − (6, −3) = (−6, 10), so c = (−3, 5). (−6, 10) forgets to halve.

3. A is the point (2, −3) and B is the point (7, 1). Find the column vector AB.

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

Answer: A. AB = position vector of B − position vector of A = (7 − 2, 1 − (−3)) = (5, 4). (−5, −4) is BA.

4. The point (2, 3) is enlarged by scale factor −2 with centre the origin. Find its image.

  1. A
    (0, 1)
  2. B
    (−1, −1.5)
  3. C
    (−4, −6)
  4. D
    (4, 6)
Show answer

Answer: C. With centre the origin, multiply each coordinate by −2: (−4, −6). A negative scale factor puts the image on the opposite side of the centre.

5. The vector p = (k, 12), written as a column vector, has magnitude 13. Given that k is positive, find k.

  1. A
    √313
  2. B
    5
  3. C
    1
  4. D
    25
Show answer

Answer: B. k2 + 122 = 132, so k2 = 169 − 144 = 25 and k = 5. Subtracting 12 from 13 gives the wrong 1.

6. OP = 2a + b, OQ = 5a + 4b and OR = 8a + 7b. Which statement is true?

  1. A
    PQ is twice as long as QR
  2. B
    PQ and QR are perpendicular
  3. C
    P, Q and R form a right-angled triangle
  4. D
    P, Q and R lie on a straight line and Q is the midpoint of PR
Show answer

Answer: D. PQ = OQ − OP = 3a + 3b and QR = OR − OQ = 3a + 3b. PQ = QR with the common point Q, so P, Q, R are collinear and Q is the midpoint.

7. The point (4, 1) is reflected in the line y = x. Find its image.

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

Answer: B. Reflecting in y = x swaps the coordinates, so (4, 1) goes to (1, 4). (4, −1) is the reflection in the x-axis.

8. A translation maps the point (2, 3) onto (−1, 7). Which column vector describes the translation?

  1. A
    (3, −4)
  2. B
    (−3, 4)
  3. C
    (1, 10)
  4. D
    (−1, 4)
Show answer

Answer: B. The vector is image minus object: (−1 − 2, 7 − 3) = (−3, 4). It moves 3 to the left and 4 up.

9. The point (3, 1) is rotated through 180° about the point (1, 1). Find its image.

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

Answer: D. From the centre (1, 1) the point is 2 right and 0 up. A half turn sends it 2 left and 0 down: (1 − 2, 1) = (−1, 1). Rotating about the origin gives (−3, −1).

10. a = (4, 1) and b = (−2, 5), written as column vectors. Find a + b.

  1. A
    (6, −4)
  2. B
    (2, 4)
  3. C
    (2, 6)
  4. D
    (−8, 5)
Show answer

Answer: C. Add the matching components: (4 + (−2), 1 + 5) = (2, 6). (6, −4) is a − b.

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Ways to practise this chapter

Transformations and vectors: questions students ask

How many Transformations and vectors MCQs are there?

27, each with the answer and a short explanation, across 3 topics: Transformations, Vectors in two dimensions, Magnitude of a vector. Every chapter test draws ten of them, so you can take it many times.

Is the O Level / IGCSE Mathematics chapter 7 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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