4. Transformations

With Cabri, you can carry out all the basic transformations – translations, rotations, reflections and enlargements.

Using the Pointer toolbox

/ The Pointer toolbox has the facility to allow for simple rotations, enlargements and a combination of the two.
It does not allow for angles or scale factors to be specified.

To rotate, draw a simple shape on a clean page – if you want to rotate about a point that is not one of its vertices you will need to create a point as well.

Select rotate from the Pointer toolbox. Next, select the point it is to be rotated around. ‘Grab’ one of the sides of the shape and drag it in a circular motion. If you press the SHIFT key whilst you drag, the dragging rotates the object in 15 intervals.

Enlargements are carried out in the same way as is the Rotate and Enlarge function.

The transformations that will be the most useful in the mathematics classroom are found in the Transform toolbox.

Transformations using the Transform Toolbox

/ The Transform toolbox allows us to carry out reflections, rotations, enlargements and translations. We can specify angles, mirror lines, scale factors, vectors etc

Reflections

To carry out a reflection it is necessary to identify the shape and the mirror line. On a clean page, draw a shape that you wish to reflect then draw a mirror line as in the diagram below.

/ From the Transform toolbox, select reflect. Click on the shape to select it, then click on the line.
The reflection will appear.
One of the sides of the polygon can be selected as the mirror line.

Any point on the original shape and the mirror line can be ‘dragged around the page and the image will move to its new position. However, the image cannot be dragged.

Translation

To carry out a translation, we need to draw a shape and create a vector for the translation.

Creation of a vector is done by selecting Vector from the Lines Toolbox. Click on the drawing area to identify the start and finish points of the vector as in the diagram below.

/ From the Transform toolbox select Translation. Click on the shape to select it then click on the vector.
The translation will then appear.
The original shape and the vector can be dragged – but not the image.

Rotation

In order for a rotation to be carried out, an object, a centre and an angle all have to be identified.

The object and the point for the centre of rotation can all be marked as before. The angle for the rotation can be identified in several ways.

In order to input an angle value we need to select Numerical Edit from the Display toolbox – this allows us to input an interactive value that can be applied to the shape. Click on the drawing area to create a text box and input the angle you require.

/ We now need to input the unit for this interactive value – degree in this case. To show the unit values available, press CTRL and U together – the list below should now appear on your page.
Click on Degree

To carry out the rotation, select Rotation from the Transform toolbox then click on the object, the centre and finally the angle value. The shape should now rotate. If you want to be sure that the centre is not accidentally moved, select Fix/Free from the Measures toolbox and click on the point to be fixed. A ‘tack’ will appear at this point and you will no longer be able to drag it around the page. To remove the tack, just repeat the process to free the point again.

Alternatively, the angle for the rotation can be identified by using an angle that has already been drawn on the page.

/ In this diagram, the angle ABC has been drawn and marked as described earlier.
The shape to be rotated is on the right of the diagram and the centre of rotation just to the left of it.

Select Rotation from the Transform toolbox. Click on the shape, the centre and then the angle marker. If the angle has not been marked, the three points that identify the angle can be clicked on instead.

Point Symmetry from the Transform toolbox rotates objects 180 about a marked point. As a test of your rotation skills, try drawing a quadrilateral and rotating it 180 about the mid point of each of its sides. If you repeat this process, you should end up with a tessellation of your quadrilateral as below.

If you drag any of the vertices of the original shape, the whole tessellation will move.

Enlargement

The Numerical Edit facility is also used to define enlargements.

On a new sheet, draw a polygon and mark a centre of enlargement (if you are not going to use one of the vertices of the shape). From the Display toolbox, Numerical Edit needs to be selected. Now click in a space on the drawing area and input the enlargement factor. As no unit is needed for an enlargement, there is no need to use the drop down menu.

To carry out the enlargement, from the Transform toolbox, select Enlargement. Click on the shape, the centre and finally the scale factor (these last two steps can be interchanged)– the enlarged shape will now appear.

/ Using Numerical Edit again, it is possible to create a diagram showing several enlargements. Negative and decimal enlargements are also possible.
Diagrams can be labelled using Text from the toolbox.

You can also double click on a value created using the numerical edit and use the up/down buttons to vary the value. If a value of 2 is showing add a .0 to make 2.0. Highlight the ‘0’ to move the value in tenths, highlight the ‘2’ to move the value in whole numbers etc

Colouring diagrams

Colouring diagrams is easy to do using the Draw menu. In the diagram below, a triangle and its reflection have been created.

/ On selecting the Draw toolbox, Fill. This displays the colour palette. Select the colour required then click on the shape that is to be filled with the chosen colour. If a second shape is to be filled, select the colour, click the shape.
/ Line colour can be changed using Draw, Colour then clicking on the required line(s).
Text colour is changed by selecting Draw, Text Colour then clicking on the text.
/ To change lines between solid and dotted select Draw, Line Style to display these options – select the required option then click on the line.
/ To change the line thickness select Draw, Thickness to display these options – select the required option then click on the line.

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