Points and Vectors

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Points and vectors may be entered via Input Bar in Cartesian or polar coordinates (see Numbers and Angles). Points can also be created using Tool New Point.gif Point tools, Tool Vector from Point.gif Vector from Point Tool, Tool Vector between Two Points.gif Vector between Two Points Tool and a variety of commands.

Note: Upper case labels denote points, whereas lower case labels refer to vectors. This convention is not mandatory.
Example:
  • To enter a point P or a vector v in Cartesian coordinates you may use P = (1, 0) or v = (0, 5).
  • In order to use polar coordinates type in P = (1; 0°) or v = (5; 90°).
Note: You need to use a semicolon to separate polar coordinates. If you don’t type the degree symbol, GeoGebra will treat the angle as if entered in radians.

In GeoGebra, you can also do calculations with points and vectors.

Example:
  • You can create the midpoint M of two points A and B by entering M = (A + B) / 2 into the Input Bar.
  • You may calculate the length of a vector v using length = sqrt(v * v)
  • If A = (a,b), then A+1 returns (a+1,b+1). If A is a complex number a+bi, then A+1 returns a+1+bi.
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