Geometry and Matrices Hands On Activity

THE REASON YOU MIGHT ACTUALLY WANT TO LEARN THIS STUFF

BY CHRISTINE LAUBER

Geometry and MatricesHands On Activity

National Standards Materials

Geometry 9 – 12 Apply transformations and use symmetry to

analyze mathematical situations understand and represent translations, reflections,

rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices;

use various representations to help understand the effects of simple transformations and their compositions.

Numbers and Operations 9 – 12 Understand meanings of operations and how

they relate to one another develop an understanding of properties of, and

representations for, the addition and multiplication of vectors and matrices;

Compute fluently and make reasonable estimates develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.

Quarter size sheets of graph paper

Graphing calculatorComputer

Animation Activity Packet

PowerPoint presentation with examples

Computer Animation

Computer Animation

First cartoons were all produced by hand.

Each slight movement required a new picture to be

drawn.

Today, computers have taken over!?

Can you name some of the computer

animated films you have seen?

What are the components of motion?

Think of how we move shapes on the

Cartesian Plane.

Translation

Rotation

Reflection

Dilation

In t

he b

egin

nin

g…

.

The first step any animator needs to do is create a simple representation of their character.

On your graph paper,

create a simple picture that

involves 5-10 points and is

NOT symmetrical.

My image will be of a kite in

the sky.

My matrix looks like this.

In order to create the picture in my TI calculator, I need to translate my matrix

into L1 and L2.

Reflects over the y-axis

Reflects over the x-axis

Rotates counterclockwise 56° Reflects over the y =

x axis

Now, change your image to a 3xn matrix by adding a last row of all 1’s

Slides 2 to the right

Slides 2 down

Slides 2 right and 3 down

Reflects over the y = x axis then slides 2 right

What about rotating the image?

Who thinks they have an idea of how to rotate the image?

Cos (5) -Sin (5)Sin (5) Cos (5)

-2.6896, 1.9924, .8716, -5.9772 7.7952, .1743, -9.9619, -.5229

-.5804, 1.9696, -1.7365, -5.90888.2258, -.3473, -9.8481, 1.0419

Cos (10) Sin (10)-Sin (10) Cos (10)