Transformations

You are going to use an Excel spreadsheet to demonstrate translation, reflection, rotation and enlargement.

Open an new Excel Workbook and create a shape which you can transform.

Step 1

Use these coordinates to make a square or you could work out the coordinates that form the initial of your name.
Make sure to put "Start Coords" over the top.

Step 2

Select both columns of data.

Click on the chart menu.

For this exercise you need the xy scatter graph with the points joined by lines

Click okay etc and fiddle with the graph if you like but you need to make a simple shape like this.

Step 3

Now type in the transformation that you are going to use on the x and y coordinates. A simple translation is the easiest one to start with.

Step 4

Now make a pair of columns for the transformed x and y coordinates of your shape.
Enter the correct formula for the transformation that you are carrying out. A formula must begin with an "=" sign. Press RETURN after you have typed the formula in.
You can drag the formula into the rest of the x column by selecting the cell and dragging its bottom right hand corner. Before you do this make the reference to your transform an absolute one by using "$" signs.

Step 5

Repeat the process for the y coordinates making sure that you use "$" signs to produce absolute references. Or type the formula into each cell individually.

Step 5

Now right click on your graph to add the final coordinates as a second data series.

Right click the graph and select "Source Data"

Then click on the "Series" tab and the "Add" button. Use the grid button at the right hand end of the x and y coordinate text boxes to select your final x and y coordinates.

The final result should look a bit like this. Fiddle with the colours scales and labels so that it looks good.

How would you modify your spreadsheet to cope with enlargement, rotation and reflection??

Hints

To enlarge a shape you could try multiplying its coordinates by 2 or 3 rather than adding something to them.

To reflect in the x axis think about what happens to the y coordinates.
You do reflections by multiplying by a certain number. What is it?