Transformations

2026 Syllabus Objectives

By the end of this topic, you should be able to:

Core Level:

  1. Recognise, describe and draw reflections in vertical or horizontal lines
  2. Recognise, describe and draw rotations about the origin, vertices or midpoints through multiples of 90°
  3. Recognise, describe and draw enlargements from a centre using positive and fractional scale factors
  4. Recognise, describe and draw translations using vectors
  5. Work with single transformations (not combinations)

Extended Level:

  1. Recognise, describe and draw reflections in any straight line
  2. Recognise, describe and draw rotations about any centre through multiples of 90°
  3. Recognise, describe and draw enlargements using positive, fractional and negative scale factors
  4. Work with combinations of transformations

What Are Transformations?

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A transformation is a way of changing the position, size, or orientation of a shape. Think of it like moving, flipping, turning, or resizing a shape on a piece of paper.

There are four main types of transformations you need to know:

  • Translation - sliding a shape from one place to another
  • Reflection - flipping a shape over a mirror line
  • Rotation - turning a shape around a fixed point
  • Enlargement - making a shape bigger or smaller from a centre point

Important Vocabulary

The object is the original shape before the transformation.

The image is the new shape after the transformation.

We label vertices (corner points) on the object with letters like A, B, C. The corresponding vertices on the image are labelled A', B', C' (read as "A prime", "B prime", "C prime").

An invariant point is a point that does not move during a transformation. It stays in exactly the same place.

Translation

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What Is Translation?

Translation means moving a shape from one position to another without rotating it, flipping it, or changing its size. Imagine sliding a book across a table - that's a translation.

The shape stays exactly the same:

  • Same size
  • Same orientation (which way up it is)
  • Just in a different position

The object and image are congruent, which means they are identical in shape and size.

How to Describe a Translation

You describe a translation using a vector. A vector is a mathematical way of showing movement.

A vector is written as a column with two numbers:

Vector = (x)
** (y)**

  • x tells you how far to move horizontally (left or right)

    • Positive x = move right
    • Negative x = move left

  • y tells you how far to move vertically (up or down)

    • Positive y = move up
    • Negative y = move down

Example: The vector (3) means move 3 units right and 1 unit down. (-1)

How to Translate a Shape

Step 1: Look at the translation vector and work out what it means.

Step 2: Take each vertex of the original shape and move it according to the vector. For example, if the vector is (3), move each point 3 squares right and 1 square down. (-1)

Step 3: Connect the new vertices to draw the image.

Step 4: Label the image with prime letters (A', B', C', etc.).

Example: If point A is at (2, 5) and you translate it by the vector (4), the new position A' will be at: (3)

  • x-coordinate: 2 + 4 = 6
  • y-coordinate: 5 + 3 = 8
  • So A' is at (6, 8)

How to Find a Translation Vector

If you're given the object and image and need to find the translation vector:

Step 1: Pick any vertex on the original shape.

Step 2: Find the corresponding vertex on the image.

Step 3: Count how many squares you move horizontally (left or right) - this is x.

Step 4: Count how many squares you move vertically (up or down) - this is y.

Step 5: Write the vector with x on top and y on the bottom, remembering to use negative numbers for left and down.

Reversing a Translation

To reverse a translation and get back to the original position, use the opposite vector. Simply change the sign of both numbers.

Example: If the translation was (6), the reverse translation is (-6). (-8) (8)

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