Project 13 Transforming Graphics with Matrices

(Revised for Windows EXCEL 2007) Project 11 – Transforming Graphics with Matrices

Print this document. The graph on the right shows the figure of a boomerang made by joining the points A ( 2, 3) B ( 1, –1) C (–2, 2) D ( 0, 1) A

Find the coordinates of the points C A’, B’, C’, D’ where each new point is obtained by multiplying the D column matrix of the coordinates of the old point by the matrix M. Then plot (and label) the new points and join them to draw the new figure. B 轾2 轾 0- 1 轾 2 A’ =M 犏 = 犏犏臌3 臌 0.5 0 臌 3

Using matrix multiplication on a straight line figure can have various effects. In this project you will study the effects of certain matrices.

1. Open the spreadsheet Fish.

2. Open the Word document Table that has a table, 8 rows by 2 columns. You will paste copies of each matrix and its associated chart into the rows of the table. 3. One at a time, enter each of the matrices below into the yellow region for matrix M by using the up/down arrow buttons.

轾0 1 轾 0 .5 轾- 1 0 轾 0 - 1 犏, 犏 , 犏 , 犏 , 臌1 0 臌- 1 0 臌 0 - 1 臌 1 0 轾0 2 轾 0.707 0.707 轾 0.866 0.5 犏, 犏 , 犏 , 臌2 0 臌- 0.707 0.707 臌 - 0.5 0.866

The transformed fish will appear. (If the graph is not big enough, follow the instructions on the spreadsheet about how to change the scale.)

4. Copy the 4 (yellow) cells of the matrix into the first row, left column, of the table in the Word document. Copy the graph (chart) to the right column of the table in the Word document. You can use Paste as Nested Table or Paste Cells. Adjust the size of the graph so that four graphs will fit on one page.

Repeat with the other matrices. BE CAREFUL: Change the matrix entries by using the up/down arrow buttons. The last two matrices will have to be entered by typing in the entries, followed by ENTER for each cell. Once that is done, the formulas for the cells are lost and the up/down arrow buttons no longer work. You can always close and reopen Fish in order to reactivate the up/down arrow buttons.

5. Mentally try to predict the effect on the fish of the matrix you used for the boomerang. Then enter the matrix and complete the table.

6. Print your Word document. Before recitation, study the table and see if you can explain why each one does what it does.