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Translation

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

In a translation (Verschiebung) a figure slides: it does not turn and keeps its size. Every point moves the same distance in the same direction.
📄 Open worksheet (PDF, German)

The video

In the video we translate a triangle with an arrow, calculate in the coordinate system and see: two reflections in parallel lines make a translation.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:14 The translation arrow
  3. 0:31 In the coordinate system
  4. 0:49 Reflecting twice
  5. 1:13 Careful, mistake!
  6. 1:33 Try it yourself

The most important points

Translation arrow

From every point an arrow goes to its image point. All arrows are equally long, parallel and point in the same direction. One arrow describes the whole translation.

The arrows from A, B, C to A', B', C'.
The arrows from \(A\), \(B\), \(C\) to \(A'\), \(B'\), \(C'\).

In the coordinate system: 3 to the right, 2 up means \((x|y) \to (x + 3|y + 2)\). \(A(1|1)\) becomes \(A'(4|3)\).

Every point goes 3 to the right and 2 up.
Every point goes 3 to the right and 2 up.

Reflecting in \(g\) and then in the parallel line \(h\) gives a translation. The arrow is twice as long as the distance between \(g\) and \(h\).

Distance 2\,\text{cm}, arrow 4\,\text{cm}.
Distance \(2\,\text{cm}\), arrow \(4\,\text{cm}\).

Careful: if the arrows have different lengths, the image is distorted. That is not a translation.

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
Page 1/5
The worksheet – Page 2
Page 2/5
The worksheet – Page 3
Page 3/5
The worksheet – Page 4
Page 4/5
Show the worksheet solutions
The worksheet – Page 5
Page 5/5

Try it yourself

Task

Translate \(P(2|1)\), \(Q(5|1)\), \(R(5|3)\) 4 to the left and 1 up. Give the image points.

Show solution

\((x|y) \to (x - 4|y + 1)\): \(P'(-2|2)\), \(Q'(1|2)\), \(R'(1|4)\).

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: translation (Verschiebung): arrow and coordinates. Give me five short tasks, one after the other. Always wait for my answer. Then tell me if it is right and explain briefly why. Use simple German sentences.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.