Change the Dog: Matrix Transformations

How does changing

a

,

b

,

c

, or

d

change the figure?

a

1

2

1

b

1

2

0

c

1

2

0

d

1

2

1

choose

dog

cat

mouse

Don Cohen, the Mathman, decided to write "Changing Shapes with Matrices" to share his interest and excitement about the ideas of changing shapes using matrices. The "dog" is taken from Don's book. I added the cat and mouse.

As you drag the sliders, ask yourself what happens when you change

a

,

b

,

c

, and

d

. Which direction does the figure move? Which numbers "flip" the figure over the

x

axis? Over the

y

axis? What numbers make the figure bigger or smaller?

If you like the transformation, select the graphic, then copy and save it in a separate file.

Don't stop there! Try some of your own on paper. Here's some graph paper. See an example of one of Don's students, Valorie, here.