Geometric Transformations Using Matrices
As we've seen in class, multiplying matrices can change every number in the resultant matrix, OR, if we multiply by the Identity Matrix, every number in the matrix can stay the same. Here, we're going to look at using Matrix Multiplication to transform geometric shapes. On the left of the screen, you'll see Matrix1 which comes from the x- and y-coordinates in the Spreadsheet on the right of the screen. Matrix2 is the Identity Matrix. Matrix3 is Matrix1 mulitplied by Matrix2. I've used the columns in Matrix1 and Matrix3 to create polygons. Try changing some of the x- and y-values in the spreadsheet. Do you see how the spreadsheet values affect the polygon? Next, try changing the Identity Matrix from 1's and 0's by making a 1 into a -1, or changing the location of the 1's and 0's. How does changing the Identity Matrix affect the polygon? What if, instead of 1, you used the number 2? What if you mixed up the numbers?