Geometry, Teacher\'s Edition

Basics of Matrices!Matrices are referred to according to its dimensions, rows by columns. To get students thinking
about which is which, use this phrase. “You row ACROSS a lake and columns hold UP houses.” By relating rowing
across and columns up, students should correctly organize the information.

Matrices can only be added if the dimensions are equivalent. Because adding matrices requires adding the same cell,
there must be equal numbers to combine.

Excel spreadsheets are excellent examples of matrices. If you have the ability to set up such spreadsheet matrices,
students can see how businesses use these to organize and manipulative inventory.

Vocabulary!A 2×1 matrix organizing a point is called apoint matrix.Thex−values should go into row 1 and the
y−values should go into row 2. The columns represent the points of the figure in the coordinate plane.

Additional Example:Target is processing its baby items inventory. Arrange the following into a matrix. Shirts:
24 − 2 T, 0 − 3 T, 9 − 4 T; shorts: 5− 4 T, 17 − 2 T, 11 − 3 T; pants: 8− 3 T, 0 − 4 T, 3 − 2 T.

Suppose another Target is shipping its excess inventory to this store. Write the sum of the two shipments into a
single matrix.

TABLE1.11:

2 T 3 T 4 T

Shirts 25 6 7

Shorts 8 19 12

Pants 1 4 30

Reflections

Pacing:This lesson should take one class period

Goal: Reflections are an important concept in geometry. Many objects can be explained with reflections. This
manipulation is also related to similarity and triangle congruence.

Matrix Multiplication!Matrix Multiplication can be quite difficult for students to compute by hand. Here is a way
to use a graphing calculator to achieve the multiplication.

a. Find the Matrix menu. If your students are using a Texas Instrument product, it is located by typing the 2nd

andx−^1 keys.

b. Edit matrix A by moving to the right to the edit menu and choosing[A]. Input the dimensions and data.

c. Choose 2nd& MODE to quit the menu

d. Repeat steps 1 – 3 for the second matrix[B].

e. Choose matrix[A]by repeating step 1 and touching enter under the Name Menu

f. Choose the multiplication symbol

g. Repeat step 7 but choose[B]instead.

h. Your working menu should look like this:[A]∗[B]

i. Touch ENTER. The answer resulting is the product of the two matrices.

Extension In-Class Activity!Reflections can be performed without a coordinate plane, just as translations.

a. Using patty paper (or tracing paper), have students draw a small scalene triangle( 4 DEF)on the right side of

the paper.

b. Fold the paper so that 4 DEFis covered.

c. Trace 4 DEF.

1.12. Transformations