GCSE MATHS • HIGHER TIER

Stretches Made Simple

Stretch points, shapes and graphs accurately in one direction using scale factors.

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Stretches in Four Moves

1

Identify

Identify whether the stretch is horizontal or vertical.

2

Find

Find the scale factor and determine which coordinate will change.

3

Multiply

Multiply only the affected coordinate by the scale factor.

4

Check

Keep the unaffected coordinate unchanged and check the transformed result.

What You’ll Learn

Understand what a stretch is.

Understand how stretches differ from enlargements.

Use scale factors correctly.

Apply vertical stretches to coordinates.

Apply horizontal stretches to coordinates.

Stretch complete shapes vertex by vertex.

Understand stretches of graphs.

Key Rules

Vertical stretch

Change the y-coordinate only. Keep the x-coordinate unchanged.
(x,y)→(x,ky)

Horizontal stretch

Change the x-coordinate only. Keep the y-coordinate unchanged.
(x,y)→(kx,y)

Worked Proof: Stretches

Step-by-Step Method

  • 1. Identify whether the stretch is horizontal or vertical.
  • 2. Find the scale factor and decide which coordinate will change.
  • 3. Multiply only the affected coordinate by the scale factor.
  • 4. Keep the unaffected coordinate unchanged and check the new coordinates.

More Worked Examples

1

Stretch the point (3, 4) vertically by scale factor 2.

Step 1 : Keep the x-coordinate.

x = 3
Step 2: Multiply the y-coordinate by 2. 4 × 2 = 8
Answer : (3, 8)

2

Stretch the point (5, 2) vertically by scale factor 3.

Step 1 : Keep the x-coordinate.

Step 2: Multiply the y-coordinate by 3.
2 × 3 = 6
Answer : (5, 6)

3

Stretch the point (4, 3) horizontally by scale factor 2.

Step 1 : Double the x-coordinate.

4 × 2 = 8
Step 2: Keep the y-coordinate.
y = 3
Answer : (8, 3)

4

Stretch the point (2, 7) horizontally by scale factor 3.

Step 1: Multiply the x-coordinate by 3.

2 × 3 = 6
Step 2: Keep the y-coordinate.
y = 7
Answer : (6, 7)
  • Common GCSE Mistakes
  • Changing both coordinates.
  • Applying the wrong scale factor.
  • Confusing stretches with enlargements.
  • Forgetting which coordinate changes.
  • Arithmetic errors when multiplying coordinates.
  • Exam Tips
  • Identify whether the stretch is horizontal or vertical first.
  • Vertical stretch: change y only.
  • Horizontal stretch: change x only.
  • Write down the scale factor before transforming coordinates.
  • Keep the unaffected coordinate unchanged.
  • Transform every vertex separately when stretching a shape.

Skills Used in Stretches

Stretches

Scale Factors

Coordinates

Vertical Transformations

Horizontal Transformations

Graph Transformations

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Printable Worksheet

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Exam-Style Questions

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Watch the Stretches Tutorial

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Frequently Asked Questions

A stretch changes the size of a shape in one direction only.

An enlargement changes dimensions proportionally, while a stretch affects only one direction.

The y-coordinate changes according to the scale factor while the x-coordinate stays unchanged.

The x-coordinate changes according to the scale factor while the y-coordinate stays unchanged.

It halves distances in the stretched direction.

Apply the stretch to every vertex separately, then join the transformed points.