Changing Shapes With Matrices

from Don's book of that name in English (1995), and in Japanese (2001), with Ms. Noriko Arai,

here using an interactive Java applet created by Fukushima Kazuhiro at IES in Japan

 The form of the multiplication of matrices used here is:

The reason Don uses this form is that all his young students have done some graphing, where the points are in the form (x,y). When he uses the matrix [x y] for the point (x,y) on the left, it is natural and easily understood. The multiplication is done by going across in the first matrix, and down in the second, multiplying, then adding.

See Valorie's work in Don's sample problems from his book.

Applet

Choose the 4 numbers for your transformation matrix below.

What happens to the dog as a result of using your transformation matrix? Do another one.

The idea for this applet is from
"Changing Shapes With Matrices"
by Don Cohen. '1995 Donald Cohen