Make two more lists of slightly longer segments that are shown at multiples of five.Īdd points displaying the numbers involved on the two number lines, or slightly above or below a number line.Write: Sequence(Text(i, (i - 0.3, -0.2)), i, -20, 20, 5)Īdjust the positions of the text elements so it looks good. By using a fifth argument to the Sequence-command, you can choose a step. The command Text(, ) creates a text of an object placed at a point. Make segments for the other line in a similar way.Įnter values for the number lines using a list of text objects. Make vertical segments along the lines, using lists of segments. You can either construct the lines using tools, or simply write y = 2 and y = -2 in the input bar. Make two lines parallel to the \(x\)-axis at \(y = 2\) and \(y = -2\). To demonstrate that \(nr1+nr2 = nr2+nr1\), you need two number lines. You will now demonstrate the addition using vectors and number lines. Use the tool Button to make a button "New numbers" and write following GeoGebra-script: SetValue(nr1, RandomBetween(1, 7)) Write nr1 = 1 and nr2 = -1 in the input bar. In order to generate a positive and a negative integer, you start by creating two variables. Exercise 5Īddition of positive and negative number using random numbers Use the tool Move to move the points defining the vector.Ĭomment: If you want to make many copies you can also use lists or the spreadsheet. Use to tool Translate by Vector to make many copies of the geometric object. Exercise 4Ĭreate a geometric object, for instance a polygon or a circle. Under the tab Advanced you can uncheck "Selection Allowed". Right-click on a point that isn't draggable and show its Properties. In order for the worksheet to be as user-friendly as possible, you can see to it that the mouse cursor only has a different appearance when hovered above the draggable point. The new points should appear above the hollow points (inside each ring). Create four new points by writing in the input bar. In the input bar of the worksheet, a point is created above the blue hollow point (inside the ring).ĭrag the point \(A\) and find the relations between coordinates for the other points. Origin, and the angle to the positive x-axis in a counterclockwise direction, the angle α. You can specify the position of a point in a Cartesian plane by specifying its distance, R, from the Given a vector \(u\) you create the unit vector using the command UnitVector(u). Given a point \(A\) and a vector \(v\), you can make a new point \(C\) by using the command Point(A,v). Given points \(A\) and \(B\) you can make the vector from \(A\) to \(B\) by using the command Vector(A, B). The vector \(u\) will be the position vector of \(A\). Given a point \(A\) you can make a vector \(u\) by using the command Point(A). The commands Point and Vector can be used to create new points/vectors from existing points/vectors. \vec\) are the vectors starting in \(O\) (the origin in this case) and ending at the point in question. If you multiply two existing vectors in the input bar, the scalar product is created and stored in a new variable. You can also create a new vector by adding or subtracting two existing vectors. Arithmeticīy multiplying an existing vector by a scalar in the input bar, you create a new vector. If you just write (x(A),y(A)+1)Ī point will be created and GeoGebra will name it. In the input bar to make a new point \(B\). As an example, given a point \(A\) you can enter B=(x(A),y(A)+1) The coordinates of a point can be used to make new points.