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Four quadrants

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

What is to the left of zero and below zero? There are the negative numbers. Then the coordinate system has four parts: the quadrants (die Quadranten).
📄 Open worksheet (PDF, German)

The video

In the video we extend the axes to the left and downwards. Then we plot points with negative coordinates.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:20 Negative numbers
  3. 0:48 Four quadrants
  4. 1:31 Plotting points
  5. 2:28 Careful, mistake!
  6. 2:51 Try it yourself

The most important points

Four quadrants

The axes divide the coordinate system into four quadrants. We count anticlockwise. The signs (die Vorzeichen): 1st \((+\,|\,+)\), 2nd \((-\,|\,+)\), 3rd \((-\,|\,-)\), 4th \((+\,|\,-)\).

The four quadrants and their signs.
The four quadrants and their signs.

Negative coordinates

Minus with x: to the left. Minus with y: down. \(P(-3\,|\,1)\): 3 to the left, 1 up.

P(-3\,|\,1), Q(-2\,|\,-4) and R(4\,|\,-3).
\(P(-3\,|\,1)\), \(Q(-2\,|\,-4)\) and \(R(4\,|\,-3)\).
T(3\,|\,-2): if you forget the minus, you end up at (3\,|\,2).
\(T(3\,|\,-2)\): if you forget the minus, you end up at \((3\,|\,2)\).

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

Try it yourself

Task

In which quadrant is the point? a) \((-5\,|\,2)\) b) \((3\,|\,-1)\) c) \((-1\,|\,-6)\)

Show solution

a) in the 2nd quadrant b) in the 4th quadrant c) in the 3rd quadrant

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: das Koordinatensystem mit vier Quadranten (negative Koordinaten, Vorzeichen, Punkte eintragen und ablesen). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

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.