Name ——————————————————————— LESSON
9.2
Date ————————————
Review for Mastery For use with pages 606–613 GOAL
Perform translations using matrix operations.
Vocabulary A matrix is a rectangular arrangement of numbers in rows and columns. An element is a number in a matrix. The dimensions of a matrix are the numbers of rows and columns, written as rows 3 columns.
EXAMPLE 1
Add and subtract matrices 1.
2.
F G F G F F G F G F F
G F
4 24 0 1 410 24 1 1 4 23 5 27 1 2 25 5 5 1 2 27 1 (25) 5 7 212 7 9 5 10
6 0 2
3 25 5 22
2 5
7 2 3 9 2 (25) 5 5 2 5 10 2 (22)
5
4 14 4 0 12 25
G
622 025
G
G
Exercises for Example 1
1.
EXAMPLE 2
f 25 9g 1 f 4 27g
2.
F G F G
LESSON 9.2
Copyright © Holt McDougal. All rights reserved.
Add or subtract.
4 5 3 26 2 9 6 5 28
Represent a translation using matrices The matrix
F
2 6 2 1
4 0
G
represents n ABC. Find the image matrix that
represents the translation of n ABC 3 units left and 2 units up. Then graph n ABC and its image. Solution
F
G
23 23 23 . 2 2 2 Add this to the polygon matrix for the preimage to find the image matrix. The translation matrix is
F
23 23 23 2 2 2 Translation Matrix
G F 1
A B C 2 6 4 2 1 0 Polygon Matrix
y
A9 B9
A9 B9 C9 21 3 1 5 4 3 2
G F
G
1
C9 A 1
B C
x
Image Matrix Geometry Chapter 9 Resource Book
173
Name ——————————————————————— LESSON
9.2
Review for Mastery
continued
For use with pages 606–613
EXAMPLE 3
Multiply matrices
F GF
G
4 25 . 22 7
2 3 6 0
Multiply
Date ————————————
Solution
The matrices are both 2 3 2, so their product is defined. Use the following steps to find the elements of the product matrix. Multiply the numbers in the 1st row of the 1st matrix by the numbers in the 1st column of the 2nd matrix. Put the result in the 1st row, 1st column of the product matrix.
F GF 2 3 6 0
STEP 2
4 25 22 7
2 3 6 0
LESSON 9.2
4 25 22 7
2 3 6 0
4 25 22 7
G
G F
2(4) 1 3(22) 2(25) 1 3(7) 5 ? ?
G
G F
2(4) 1 3(22) 2(25) 1 3(7) 5 6(4) 1 0(22) ?
G
Multiply the numbers in the 2nd row of the 1st matrix by the numbers in the 2nd column of the 2nd matrix. Put the result in the 2nd row, 2nd column of the product matrix.
F GF 2 3 6 0
STEP 5
? ?
Multiply the numbers in the 2nd row of the 1st matrix by the numbers in the 1st column of the 2nd matrix. Put the result in the 2nd row, 1st column of the product matrix.
F GF
STEP 4
2(4) 1 3(22) 5 ?
Multiply the numbers in the 1st row of the 1st matrix by the numbers in the 2nd column of the 2nd matrix. Put the result in the 1st row, 2nd column of the product matrix.
F GF
STEP 3
G F
4 25 22 7
G F
2(4) 1 3(22) 2(25) 1 3(7) 5 6(4) 1 0(22) 6(25) 1 0(7)
Simplify the product matrix.
F
2(4) 1 3(22) 2(25) 1 3(7) 6(4) 1 0(22) 6(25) 1 0(7)
G F
2 11 5 24 230
G
G
Exercises for Examples 2 and 3
F
G
0 1 5 6 represents quadrilateral JKLM. 1 22 0 2 Write the translation matrix that represents the translation of JKLM 3 units right and 4 units down. Then graph quadrilateral JKLM and its image.
3. The matrix
Multiply. 4.
174
Geometry Chapter 9 Resource Book
F GF G 2 0 0 22
1 23
9 5
5.
F G
f 6 2g 28 27
6.
F
GF G
26 1 1 21
3 25 4 1
Copyright © Holt McDougal. All rights reserved.
STEP 1
Lesson 9.2, continued
F F
217.3 16. 220 A B 26 2 19. 1 2
G F G
F
23 7 233 0
G
215 17. [23] 18. 26 C D 21 28 25 26
210 6
G
A B 21 1 20. 5 7
C D E 6 8 0 5 2 1
F
G
A B C G 23 22 2 1 2. 21 4 5 23
G F
F
5.
F
F G
4 212
4 5 7 6. 21 28 23
8.
F
5.3 12.2 2.8 10.4
10.
1 4
3
1
3
5 2
3
}
6 10 22 1
G
M9
C
G
FG F G 5 4 3
37 24. 43 40
25. team 2; 43
Review for Mastery 1. f 21
F
2g 2.
3 3 24 24
F
21 211 24 214
G
3 24
3 24
G y 4
M x
J K
J9
L
8
M9
L9 K9
F
2 18 6 210
G
5. f 262g 6.
F
214 31 21 26
2. x 5 2, y 5 25, z 5 9
3 3. x 5 21, y 5 }, z 5 4 2
6
N9 O9
4. x 5 6, y 5 210, z 5 3 M P
2
A9
x
5. x 5 21, y 5 3, z 5 2 6. x 5 2, y 5 17, z 5 3
O
C9 x
7.
F G
Geometry Chapter 9 Resource Book
21 5 f 229g 24
Challenge Practice
F
29 23 4 11 12. f 220g 13. 14. 7 2 12 3 2 1 21.3 1 0 15. 16. f 224g 17. 0.9 226 8
A28
F G
6g
G
1. Men: $993; Women: $810 2. Men: $1620; Women: $1764
4
N
F G
G
1. x 5 3, y 5 24, z 5 2
P9
1
23.
4.
y
B9 1
F 0 4
Problem Solving Workshop: Using Alternative Methods
2 }2 2 }2 7.
11. B
E 5 0
G
G
G F 9.
y
A
F
3.
A B C D E F G 23 22 2 4 6 5 1 3. 21 2 5 4 1 21 23 3g
D 9 21
and your friend can buy 1 video game.
Practice Level C
4. f 10
A B C 1 8 12 19. 6 7 4
G
21. x 5 2.5, y 5 24 22. You can buy 3 DVDs
s 5 21; (210, 7), (24, 21), (23, 6) 22. Office 1: $670; Office 2: $890 23. a. First night: 590, second night: 785, third night: 830 b. First night: $2575, second night: $3385, third night: $3565
F
F
20. Sample answer: f 5
21. x 5 28, y 5 4, b 5 4, c 5 5, d 5 3, r 5 210,
E F G 6 5 1 1. 1 21 23
A B C 211 27 23 18. 24 4 0
F
G
G
F 3
6 21 21 0 23 8 4 23 11
G F 4 8.
210 0 9 3 9 212 9. 212 26 8 20 225 28
5 21 1 7 4 5
5 11 6
G
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ANSWERS
13. [230] 14. [28.8] 15.
