GCSE MATHS • HIGHER TIER

Translation Made Simple

Move points and shapes accurately across coordinate grids using translation vectors.

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Translation in Four Moves

1

Read the Vector

Identify the horizontal and vertical movement shown by the translation vector.

2

Move Horizontally

Use the first vector value: positive moves right and negative moves left.

3

Move Vertically

Use the second vector value: positive moves up and negative moves down.

4

Plot and Check

Plot every translated point and check that size, shape and orientation are unchanged.

What You’ll Learn

Understand what a translation is.

Recognise the key features of translations.

Read and interpret translation vectors.

Use positive and negative vector values.

Translate points and complete shapes.

Describe a translation using a vector.

Distinguish translations from other transformations.

Key Rules

Translation vector

A translation is described using a vector showing horizontal and vertical movement.

First number

The first number shows horizontal movement: positive = right, negative = left.

First number

The first number shows horizontal movement: positive = right, negative = left.

Using the radius

Arc Length = (Angle ÷ 360) × 2πr

Shape stays unchanged

A translation keeps the same size, shape and orientation. Every point moves the same distance in the same direction.

Worked Proof: Translation

Key Features of Translations

  • The shape keeps the same size.
  • The shape keeps the same shape.
  • The shape does not rotate.
  • The shape does not flip.
  • Every point moves the same distance in the same direction.

More Worked Examples

1

Translate the point (5, 7) by the vector (-2, 3).

Move 2 units left and 3 units up.

(5 - 2, 7 + 3)
= (3, 10)
Answer: (3, 10).

2

Translate the point (-1, 4) by the vector (5, -2).

(-1 + 5, 4 - 2)

= (4, 2)
Answer: (4, 2).

3

Translate the point (8, 2) by the vector (-3, -4).

(8 - 3, 2 - 4)

= (5, -2)
Answer: (5, -2).

4

Translate the point (8, 2) by the vector (-3, -4).

(8 - 3, 2 - 4)

= (5, -2)
Answer: (5, -2).
  • Common GCSE Mistakes
  • Confusing left and right movement.
  • Moving the shape the wrong distance.
  • Confusing positive and negative values.
  • Rotating the shape accidentally.
  • Writing vectors incorrectly.
  • Exam Tips
  • Read the horizontal vector value first.
  • Positive horizontal values move right; negative values move left.
  • Positive vertical values move up; negative values move down.
  • Keep the shape’s size and orientation unchanged.
  • When describing a translation, state the vector clearly.

Skills Used in Translation

Transformations

Coordinates

Translation Vectors

Positive & Negative Numbers

Accurate Plotting

Graph Transformations

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Watch the Translation Tutorial

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Frequently Asked Questions

A translation moves a shape without changing its size, shape or orientation.

It shows horizontal movement.

It shows vertical movement.

A negative horizontal value moves left and a negative vertical value moves down.

State the translation vector.

No. The shape keeps the same orientation.