[PDF] 9-4 - Study Guide and Intervention

View - Download 9-4 - Study Guide and Intervention

Previous PDF

Next PDF

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Lesson 9-4

Chapter 9 25 Glencoe Geometry

Glide Reflections When two transformations are applied to a figure, one after another, the total transformation is a composition of transformations. A glide reflection is a translation followed by a reflection in a line parallel to the translati on vector. Notice that the composition of isometries is another isometry. Triangle ABC has vertices A(3, 3), B(4, -2) and C(-1, -3). Graph ABC and its image after a translation along

2, -1? and a reflection in the

x -axis.

Step 3

Graph ABC and its image A B C

Exercises

Triangle XYZ has vertices X(6, 5), Y(7, -4) and Z(5, -5). Graph ?XYZ and its image after the indicated glide reflection.Study Guide and Intervention

Compositions of Transformations

Example

Step 1

translation along

2, -1?

x , y) → (x - 2, y - 1) A (3, 3) → A?(1, 2) B (4, -2) → B?(2, -3) C

1, -3) → C?(-3, -4)Step 2 reflection in the x-axis.

x , y) → (x, -y) A (1, 2) → A?(1, -2) B (2, -3) →

B?(2, 3)

C

3, -4) → C?(-3, 4)y

x

1. Translation: along ?1, 2?

Reflection: in

y -axis

3. Translation: along ?2, 0?Reflection: in x = y 2. Translation: along ?-3, 4? Reflection: in x-axis

4. Translation: along ?-1, 3? Reflection: in x-axis

y x"""" y x 9-4 -22

2-2-4-6-8

-104 6 810
4 6 8

1046810

xy 22

2-2-4-6-8

104
6 810
4 6 8

1046810y

x Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Chapter 9 26 Glencoe Geometry

9-4 Compositions of Reflections The composition of two reflections in parallel lines is the same as a translation. The compositions of two reflections in inters ecting lines is the same as a rotation.

Copy and reflect figure A in line ? and then line

m. Then describe a single transformation that maps A onto A Step 1 Reflect A in line ℓ. Step 2 Reflect A? in line m. m m m The compositions of two parallel lines is the same as a translation.

Exercises

Copy and reflect figure

P in line a and then line b . Then describe a single transformation that maps P onto P 1. a b 2. a b

50°

3. a b 4. ab

125°

Study Guide and Intervention (continued)

Composition of Transformations

Example

rotation 180

°rotation 100°

translation rotation 250quotesdbs_dbs21.pdfusesText_27

[PDF] 9 3 study guide and intervention arcs and chords answers

[PDF] 9 3 study guide and intervention circles

[PDF] 9 3 study guide and intervention circles answers

[PDF] 9 3 study guide and intervention factoring trinomials

[PDF] 9 3 study guide and intervention graphing rational functions answers

[PDF] 9 3 study guide and intervention graphing reciprocal functions answers

[PDF] 9 3 study guide and intervention rotations

[PDF] 9 3 study guide and intervention rotations answers

[PDF] 9 3 study guide and intervention solving quadratic equations by graphing

[PDF] 9 3 study guide and intervention transformations of quadratic functions

[PDF] 9 3 study guide and intervention transformations of quadratic functions answers

[PDF] 9 3 study guide and intervention trigonometric functions of general angles

[PDF] 9 4 practice factoring trinomials ax2+bx+c

[PDF] 9 4 skills practice factoring trinomials ax2+bx+c

[PDF] 9 4 skills practice solving quadratic equations by factoring answer key