1. Using grids

The graph function on Cabri is fairly basic. Lines, circles and conics can be drawn and their equations found. Gradients of lines can also be found. Coordinates of points can also be displayed. Probably the main use that the grid function can be put to is to demonstrate transformations.

Setting up the axes

Open a new page.

/

From the Draw toolbox select Show axes. This will create a Cartesian grid. Hide axes will replace Show axes in the Draw toolbox and does just what it says!

Click on the Pointer toolbox. If you now grab the origin, you can translate it to any place on the grid.
If you wish to change the scale on both the axes, drag the first scale mark on the x-axis to the required position. If you only want to change the y-axis scale, drag the first mark on the y-axis.

The axes can also be rotated. To rotate both axes, grab the x-axis beyond the first mark. To rotate the y-axis, just grab the axis beyond the first mark.

/ If you want to have a grid system visible as well as the axes, select Define Grid from the Draw toolbox. Then click on one of the axes.
To hide the grid system, select the Pointer toolbox then just click on any one of the grid points - all the points will start to flash, now just press Delete.

Plotting points

To plot points on the grid, just mark them using the Points toolbox. If you want to change the colour of the points you create, use Colour from the Draw toolbox to bring up the palette of colours available. When you have selected the colour, just click on each of the points to change it.

If the coordinate of the point needs to be visible, select Equation or Coordinates from the Measures toolbox – click on each point and the coordinates will appear. Coordinates can be given to 1d.p. by going to Options, Preferences, Display precision of units. From this go to the drop down menu labelled Other – set to 1 for 1d.p., 0 for integers etc

Drawing lines

Lines can be drawn on the grid by plotting points first then joining with the Line tool or by using the Line tool to draw lines straight onto the grid. You cannot find the equation of a line drawn using either the Ray or Segment tools.

/ Once a line is drawn its equation can be displayed by selecting Equation or Coordinates from the Measures toolbox then clicking on the line.
Selecting Slope will give the gradient as long as both axes have the same scale.
Selecting Equation or Coordinates will give the coordinate of a point marked using the Points toolbox.

The position of any line on the grid can be changed by dragging. If the line was defined by two points, grab one of the points and the line will rotate around the point not being dragged.

A line defined using the Line tool can be dragged using the defining point in which case it moves parallel to the original line. If the line is grabbed, it will rotate around the defining point. When a line is dragged any equation, coordinate, slope will update.

Circles and conics can be drawn on the axes using the Curves toolbox. The equation can be found in the same ways as that of a line.

Coordinates of points of intersection of lines, circles etc can be found by marking the intersection(s) with a point(s) using the Points toolbox – then selecting Equation and Coordinates from the Measure toolbox.

Grids and transformations

All transformations as described in the transformation section can be carried out on the grids.

/ This diagram shows successive rotations of 90 of the triangle in the first quadrant. Note that Numerical Edit is used to display the 90 first.
To see other rotations of the triangle, double click on the angle to show the text box and as you change the angle the diagram will change.
/ This is what happens when the angle in the above diagram is changed to 40.
/ This is a reflection of a polygon in the line y=x.

Try out other transformations using the grids. Label diagrams, show coordinates, change line colours, fill colours etc

Drawing graphs of functions

The graph of any function can be drawn using Cabri – but it is not a simple process! It is possibly something you could use as a demonstration – but not something you would want the pupils to do.

Let’s say we want to draw the graph of y=x2-5.

First we need to draw the axes by selecting Show Axes from the Draw toolbox.

From the Display toolbox, select Expression – a text box will appear allowing the function to be typed in – in this case x^2-5.

Next, mark a point anywhere on the x-axis but not where x is an integer value and not too far from the origin. Display the coordinates of this point using Equation or Coordinates from the Display toolbox.

Now from the Display toolbox select Evaluate an expression

-click on the function

-then click on the x value of the coordinate

-the function will now be evaluated – drag the answer box out of the way and click to display it on the screen.

This value now needs to be marked on the y-axis. To do this, select Measurement transfer from the Construct toolbox

-click on the value just created

-click on the y-axis

-this will put a point on the y axis – this is the value of the function with the value of x substituted

Now, using either the parallel or perpendicular tools, construct lines through the two points on the axes and mark their point of intersection. Your diagram will now look something like the one below.

/ Function
Lines constructed through the marked points
Value of function

Point of intersection

From the Construct menu select Locus. Click on the point just created (the intersection), then click on the point on the x axis. The curve should be created.

See the diagram on the next page.

/ By grabbing and dragging the initial point marked on the x-axis, you can see the x and y values of any point on the curve.

The same stages can be carried out to create the graph of any function!

1