Skip to content

Paper Together: sit a paper in a room with your friends.See how it works

Enlarging with negative scale factors practice questions with answers

Higher · Grade 6 · Non-calculator

A second set of enlarging with negative scale factors 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

Enlarge the point (2, 1) with scale factor -3 and centre (0, 0). Write down the image.

Show answer

Answer: (-6, -3)

  1. Multiply 2 by -3 to get -6.
  2. Multiply 1 by -3 to get -3.
  • Method (1): Multiply 2 by -3 to get -6.
  • Accuracy (1): Multiply 1 by -3 to get -3.

Question 2 Easy

Enlarge the point (0, 3) with scale factor -2 and centre (0, 0). Write down the image.

Show answer

Answer: (0, -6)

  1. Multiply 0 by -2 to get 0.
  2. Multiply 3 by -2 to get -6.
  • Method (1): Multiply 0 by -2 to get 0.
  • Accuracy (1): Multiply 3 by -2 to get -6.

Question 3 Medium

An enlargement with centre (0, 0) maps (1, 4) to (-3, -12). Find the scale factor.

Show answer

Answer: -3

  1. Divide -3 by 1 to get -3.
  2. Verify -12 / 4 = -3.
  • Method (1): Divide -3 by 1 to get -3.
  • Accuracy (1): Verify -12 / 4 = -3.

Question 4 Medium

An enlargement with centre (0, 0) maps (5, 1) to (-5, -1). Find the scale factor.

Show answer

Answer: -1

  1. Divide -5 by 5 to get -1.
  2. Verify -1 / 1 = -1.
  • Method (1): Divide -5 by 5 to get -1.
  • Accuracy (1): Verify -1 / 1 = -1.

Question 5 Hard

Which quadrant contains the image of (3, 1) after scale factor -2?

Show answer

Answer: third

  1. Both coordinates change from positive to negative.
  2. The image point (-6, -2) lies in the third quadrant.
  • Method (1): Both coordinates change from positive to negative.
  • Accuracy (1): The image point (-6, -2) lies in the third quadrant.

Question 6 Hard

Which quadrant contains the image of (4, 2) after scale factor -1?

Show answer

Answer: third

  1. Both coordinates change from positive to negative.
  2. The image point (-4, -2) lies in the third quadrant.
  • Method (1): Both coordinates change from positive to negative.
  • Accuracy (1): The image point (-4, -2) lies in the third quadrant.

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

Enlarge the point (2, 5) with scale factor -3 and centre (0, 0). Find the image.

Show answer

Answer: (-6, -15)

  1. Multiply the x-coordinate by -3: 2 × -3 = -6.
  2. Multiply the y-coordinate by -3: 5 × -3 = -15.
  3. Combine into coordinates: (-6, -15).
  • Method (1): Multiplies one coordinate by -3 correctly
  • Accuracy (1): Image (-6, -15)

Quick checks

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

Check 1

Negative scale factor does what to a first-quadrant point?

Show answer

It multiplies by a negative factor, sending both coordinates negative. It multiplies by a negative factor, sending both coordinates negative.

Check 2

Scale factor -2, centre (0, 0). The image of (3, 1) is

  1. (-6, -2)
  2. (-4, 2)
  3. (-6, -3)
Show answer

(-6, -2) Multiply both 3 and 1 by -2 to get (-6, -2).

Check 3

Scale factor -1, centre (0, 0). The image of (4, -2) is

  1. (-4, 2)
  2. (-6, -2)
  3. (-6, -3)
Show answer

(-4, 2) Multiply both 4 and -2 by -1 to get (-4, 2).

Check 4

Scale factor -3, centre (0, 0). The image of (2, 1) is

  1. (-6, -3)
  2. (-6, -2)
  3. (-4, 2)
Show answer

(-6, -3) Multiply both 2 and 1 by -3 to get (-6, -3).

Check 5

From (3, 1) across to (-6, -2), the scale factor is

  1. 4
  2. -2
  3. -3
Show answer

-2 Divide image coordinate by object coordinate: -6 / 3 = -2.

Check 6

From (4, 2) across to (-12, -6), the scale factor is

  1. -3
  2. 6
  3. 3
Show answer

-3 Divide image coordinate by object coordinate: -12 / 4 = -3.

Check 7

(3, 1) is enlarged with scale factor -2 and centre (0, 0). How far is the image from the origin?

Show answer

Object distance is √10, then doubled to 2√10. Object distance is √10, then doubled to 2√10.

Check 8

(6, 8) is enlarged with scale factor -2 and centre (0, 0). How far is the image from the origin?

  1. 3
  2. 2
  3. 20
Show answer

20 Pythagoras gives 10, then times 2 is 20.

Check 9

First-quadrant object and scale factor -2 land in which quadrant?

Show answer

Both positive values become negative in the third quadrant. Both positive values become negative in the third quadrant.

Check 10

Scale factor -2, centre (0, 0). The image of (0, 3) is

  1. (-4, 2)
  2. (0, -6)
  3. (-6, -3)
Show answer

(0, -6) 0 times -2 is 0 and 3 times -2 is -6.

Check 11

Why is (6, 2) wrong for scale factor -2 on (3, 1)?

Show answer

The negative factor flips the signs through the origin. The negative factor flips the signs through the origin.

Check 12

Dividing an image coordinate by the object coordinate gives the

Show answer

Image over object gives the enlargement scale factor. Image over object gives the enlargement scale factor.

Check 13

√(3²+1²) simplified, then doubled, is

Show answer

Distance √10 times 2 is 2√10. Distance √10 times 2 is 2√10.

Check 14

Same size, opposite direction, from (2, 5) to (-2, -5). The scale factor is

  1. 7
  2. 4
  3. -1
Show answer

-1 Direction reverses without changing size: -1.

Check 15

Enlargement from the origin multiplies coordinates by the scale factor. Does it add?

Show answer

Enlargement multiplies coordinates by the scale factor; it never adds to them. Enlargement multiplies coordinates by the scale factor; it never adds to them.

Keep going with Enlarging with negative scale factors

Practise free

Start free

AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.

Next topicPractise free