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How to carry out transformations on shapes

Part of Mathematics and NumeracyPractise and revise KS2 maths

Introduction to transformations on different shapes

A girl studying transformations on shapes for the SEAG transfer test

This page has been put together to help you practise and revisit some of the brilliant skills you’ve learned all through primary school.

It’s a great way to boost your confidence in Maths and get you ready for the exciting next step into Year 8!

Let's move those shapes!

Complete this page and you’ll discover:

  • the 3 ways to transform (move) a shape: rotation (turn), reflection (flip), and translation (slide)
  • how to fully describe a rotation using its angle, direction, and centre
  • how transformations are linked to coordinates on a grid
  • how to perform multi-step transformations (one move after another)
A girl studying transformations on shapes for the SEAG transfer test
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The three transformations

A yellow L shape is to the left. Four squares to the right and one square down is a turquoise L shape. Useful for pupils studying for the SEAG transfer test

A transformation is a specific way to move a shape on a grid without changing its size.

  1. Translation (slide) This is the simplest move. The shape just slides to a new position. It doesn't turn or flip.

How to describe it: you just need directions, eg "Translate 5 squares right and 2 squares up."

A yellow L shape is to the left. Four squares to the right and one square down is a turquoise L shape. Useful for pupils studying for the SEAG transfer test
Diagram showing reflection of a shape. A lilac L shape on the left is reflected in a mirror line, a yellow backwardsnL shape is shown as a reflection to the right of the mirror line. Useful for pupils studying for the SEAG transfer test
  1. Reflection (flip) The shape is flipped over a 'mirror line' (also called a 'line of reflection').

How to describe it: you just need the position of the mirror line, eg "reflect in the y-axis" or "reflect in the x-axis."

Diagram showing reflection of a shape. A lilac L shape on the left is reflected in a mirror line, a yellow backwardsnL shape is shown as a reflection to the right of the mirror line. Useful for pupils studying for the SEAG transfer test
Image demonstrating rotation. A yellow L shape is to the left. Three squares to the right another yellow L shape which has been rotated 90 degrees. Useful for pupils studying for the SEAG transfer test
  1. Rotation (turn) This is a turn. It is the most complex transformation because it needs three pieces of information.
  • Angle. How far to turn (eg 90°, 180°).
  • Direction. Clockwise or anti-clockwise.
  • Centre of rotation. The point the shape spins around (eg the origin (0,0) or a corner of the shape).
Image demonstrating rotation. A yellow L shape is to the left. Three squares to the right another yellow L shape which has been rotated 90 degrees. Useful for pupils studying for the SEAG transfer test
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Multi-Step transformations

A multi-step problem asks you to do two or more transformations, one after the other.

The order is very important!

"Translate then reflect" can give a different result than "Reflect then translate".

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Coordinate transformation

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Summary

You've mastered transformations! You can now move a shape in three different ways:

Translation (a slide, described with directions like 'right' and 'up').

Reflection (a flip, described with a mirror line).

Rotation (a turn, described with an angle, direction, and centre).

You also know how to work with coordinates and follow multi-step instructions.

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Brain boost

Think about these questions to stretch your thinking and sharpen your skills!

  • What is the only piece of information you need to describe a Translation?

  • What are the three pieces of information you always need to describe a Rotation?

  • "A 180° rotation is the same as a reflection." Is this statement true or false? Why?

Have a chat about your answers with a parent, teacher or your class.

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