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Transformations practice questions with answers

Foundation and Higher · Grade 3 · Non-calculator

A second set of transformations questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

The point (3, 7) is reflected in the x-axis. What are the image coordinates?

Show answer

Answer: (3, -7)

  1. Reflection in the x-axis keeps x the same and changes the sign of y.
  2. (3, 7) goes to (3, −7).
  • Method (1): Reflection in the x-axis keeps x the same and changes the sign of y.
  • Accuracy (1): Answer (3, -7)

Question 2 Easy

The point (4, −2) is translated by the vector (5, 1). What are the image coordinates?

Show answer

Answer: (9, -1)

  1. The vector (5, 1) moves x by 5 and y by 1.
  2. New x: 4 + 5 = 9. New y: −2 + 1 = −1.
  • Method (1): The vector (5, 1) moves x by 5 and y by 1.
  • Accuracy (1): Answer (9, -1)

Question 3 Medium

The point (0, 4) is translated by the vector (−4, −3). What are the image coordinates?

Show answer

Answer: (-4, 1)

  1. The vector (−4, −3) moves x by −4 and y by −3.
  2. New x: 0 + (−4) = −4. New y: 4 + (−3) = 1.
  • Method (1): The vector (−4, −3) moves x by −4 and y by −3.
  • Accuracy (1): Answer (-4, 1)

Question 4 Medium

The point (1, 6) is rotated 90° clockwise about the origin. What are the image coordinates?

Show answer

Answer: (6, -1)

  1. A 90° clockwise turn about the origin sends (x, y) to (y, −x).
  2. (1, 6) goes to (6, −1).
  • Method (1): A 90° clockwise turn about the origin sends (x, y) to (y, −x).
  • Accuracy (1): Answer (6, -1)

Question 5 Hard

The point (4, 1) is rotated 90° clockwise about the origin. What are the image coordinates?

Show answer

Answer: (1, -4)

  1. A 90° clockwise turn about the origin sends (x, y) to (y, −x).
  2. (4, 1) goes to (1, −4).
  • Method (1): A 90° clockwise turn about the origin sends (x, y) to (y, −x).
  • Accuracy (1): Answer (1, -4)

Question 6 Hard

The point (−2, 3) is reflected in the x-axis. What are the image coordinates?

Show answer

Answer: (-2, -3)

  1. Reflection in the x-axis keeps x the same and changes the sign of y.
  2. (−2, 3) goes to (−2, −3).
  • Method (1): Reflection in the x-axis keeps x the same and changes the sign of y.
  • Accuracy (1): Answer (-2, -3)

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

The point (0, 7) is rotated 90° clockwise about the origin. What are the image coordinates?

Show answer

Answer: (7, 0)

  1. A 90° clockwise turn about the origin sends (x, y) to (y, −x).
  2. (0, 7) goes to (7, 0).
  3. The image is (7, 0).
  • Method (1): A 90° clockwise turn about the origin sends (x, y) to (y, −x).
  • Accuracy (1): Answer (7, 0)

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

The point (4, 4) is reflected in the x-axis. What are the image coordinates?

  1. (4, -4)
  2. (-4, 4)
  3. (4, 4)
Show answer

(4, -4) The result is (4, -4).

Check 2

The point (−2, 6) is translated by the vector (−4, −3). What are the image coordinates?

  1. (-6, 3)
  2. (2, 9)
  3. (-5, 2)
Show answer

(-6, 3) The result is (-6, 3).

Check 3

The point (−1, −3) is rotated 90° clockwise about the origin. What are the image coordinates?

  1. (-3, 1)
  2. (3, -1)
  3. (-3, -1)
Show answer

(-3, 1) The result is (-3, 1).

Check 4

The point (5, −1) is reflected in the x-axis. What are the image coordinates?

  1. (5, 1)
  2. (-5, -1)
  3. (-1, 5)
Show answer

(5, 1) The result is (5, 1).

Check 5

The point (1, 1) is translated by the vector (3, −2). What are the image coordinates?

  1. (4, -1)
  2. (-2, 3)
  3. (-1, 4)
Show answer

(4, -1) The result is (4, -1).

Check 6

The point (2, 3) is rotated 90° clockwise about the origin. What are the image coordinates?

  1. (3, -2)
  2. (-3, 2)
  3. (3, 2)
Show answer

(3, -2) The result is (3, -2).

Check 7

The point (3, 5) is reflected in the x-axis. What are the image coordinates?

  1. (3, -5)
  2. (-3, 5)
  3. (5, 3)
Show answer

(3, -5) The result is (3, -5).

Check 8

The point (4, 7) is translated by the vector (−2, 4). What are the image coordinates?

  1. (2, 11)
  2. (6, 3)
  3. (8, 5)
Show answer

(2, 11) The result is (2, 11).

Check 9

The point (−2, −2) is rotated 90° clockwise about the origin. What are the image coordinates?

  1. (-2, 2)
  2. (2, -2)
  3. (-2, -2)
Show answer

(-2, 2) The result is (-2, 2).

Check 10

The point (−1, 8) is reflected in the x-axis. What are the image coordinates?

  1. (-1, -8)
  2. (1, 8)
  3. (8, -1)
Show answer

(-1, -8) The result is (-1, -8).

Check 11

The point (0, 2) is translated by the vector (5, 1). What are the image coordinates?

  1. (5, 3)
  2. (-5, 1)
  3. (1, 7)
Show answer

(5, 3) The result is (5, 3).

Check 12

The point (1, 4) is rotated 90° clockwise about the origin. What are the image coordinates?

  1. (4, -1)
  2. (-4, 1)
  3. (4, 1)
Show answer

(4, -1) The result is (4, -1).

Check 13

The point (2, 6) is reflected in the x-axis. What are the image coordinates?

  1. (2, -6)
  2. (-2, 6)
  3. (6, 2)
Show answer

(2, -6) The result is (2, -6).

Check 14

The point (3, −3) is translated by the vector (−4, −3). What are the image coordinates?

  1. (-1, -6)
  2. (7, 0)
  3. (0, -7)
Show answer

(-1, -6) The result is (-1, -6).

Check 15

The point (4, −1) is rotated 90° clockwise about the origin. What are the image coordinates?

  1. (-1, -4)
  2. (1, 4)
  3. (-1, 4)
Show answer

(-1, -4) The result is (-1, -4).

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