When entering data in a spreadsheet, just highlight the cell and type. You'll notice that what you type is at the top of the screen. When you press Enter the value or word appears in the cell.
When entering formulas, type = or + or @ depending on your spreadsheet and then the formula. For example: In ClarisWorks, if you highlight C5 and type =A2+5 the spreadsheet will add 5 to the contents of
cell A2and place the answer in cell C5.
Spreadsheets use formulas in which they represent variables by cell addresses. For example: if you want to add the value 100 in
cell A3and the value 28 in cell B3and you want the answer to appear in cell D7,you would highlight cell D7and type =A3+B3 and hit Enter.
For ClarisWorks users: If you haven't done so already, set your Web browser to use ClarisWorks as a helper application for these examples, and then open this spreadsheet to practice entering formulas.
For Microsoft Excel users: Set up your browser to use Excel as a helper application; then open this spreadsheet to practice.
For those who do not have an active spreadsheet, Jan Garner's Spreadsheet Basics is a good introduction.
For this example we will use the transformation matrix:
Open a new spreadsheet window and type your transformation matrix into cells A1, A2, B1, and B2 as shown.
A B 1 3 -2 2 4 1
Next, enter the coordinates of the points O, A, B, and C in cells D1 to D5 and E1 to E5.
- Notice that the x coordinates are in column D and the y coordinates in column E.
- It is important for graphing purposes to close up the figure. Thus
point Ois written twice, at the top of the list, and again at the bottom.
... D E 1 ... 0 0 2 ... 1 0 3 ... 1 1 4 ... 0 1 5 ... 0 0
Next, enter the formulas to multiply the transformation matrix by the vectors that represent the points.
- In cell D7 type the following: =($A$1*D1)+($B$1*E1)
- In cell E7 type: =($A$2*D1)+($B$2*E1)
Note: the $ signs are very important. They create absolute references which signify that the formula will always use the information in cells A1 and B1.
ClarisWorks users: You may open this spreadsheet to see data and formulas already entered and to practice entering others.
Microsoft Excel users: You may open this spreadsheet.
If you do not have an active spreadsheet, please examine the table below. If you entered the formulas correctly you should have the results shown:
D E 7 0 0 8 3 4 9 1 5 10 -2 1 11 0 0
Now graph your two shapes by selecting all cells from D1 down to D11 and across to highlight E1 to E11. Select Make Chart and then choose an x-y plot and adjust the axes so that the original square is a square.
Applying the Transformation
Experiment with change your transformation matrix by typing new values into one or more of the cells A1, A2, B1 and B2. Watch the change in the image coordinates and in your chart window.
Scale Note: The scale is very important to give an accurate view of the results. To ensure that all square figures actually show up as squares, adjust the x or y-axis scaling until they are equal. (Or adjust the monitor display until a square looks square.)
Back to Linear Transformations using Spreadsheets
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