What are translation, rotation and reflection?

  • Shapes can be transformed in a number of ways. These include translation, rotation and reflection.

  • Translation and rotation cause a shape to move.

  • Reflection causes a shape to replicate itself.

A short video demonstrating translation, rotation and reflection.

Translation, rotation and reflection are examples of mathematical operations that you can perform on an object.


When translating a shape, you can move it up or down or from side to side, but you cannot change its appearance in any other way. When a shape is translated, each of the vertices (corners) must be moved in exactly the same way.


If you put a sheet of paper on a table and place your pen in the middle of it, you can rotate the paper whilst keeping the pen in a fixed position. The pen is acting as a centre of rotation and you can rotate an object around it, anywhere between 0° and 360°.


If you look in a mirror, you see your own image. You (the object) and your image appear to be the same distance and angle from the mirror. The mirror acts as a line of reflection, through which your image is copied.