______________________ Name

MATH 2020

Final Countdown Unit 2

Pages Due

Lesson 1 ___________________

Lesson 2 ___________________

Lesson 3 ___________________

Lesson 4 ___________________

Lesson 5 ___________________

Lesson 6 ___________________

Lesson 7 ___________________

b

Key Vocabulary '4 congruent figures,

p. 44

corresponding angles,

p. 44

corresponding sides,

p. 44

EXAMPLE ,J

<IDffllOO'@ffl� Lesson Tutorials '¥

BigideasMath

'.J Key Idea Congruent Figures

Figures that have the same size and the same shape are called congruent figures. The triangles below are congruent.

Matching angles are called corresponding angles.

Matching sides are called corresponding sides.

The figures are congruent. Name the corresponding angles and the

corresponding sides.

Corresponding Angles

LAandLW

LBandLX

LC and LY

LD and LZ

Corresponding Sides

Side AB and Side WX

Side BC and Side XY

Side CD and Side YZ

Side AD and Side WZ

_L 7· D C

• On Your Own

� Y.o,u're Re d ...,,_a_ Y

Exercises 6 and 7

The symbol= means iscongruent to.

1. The figures are congruent.Name the corresponding anglesand the corresponding sides.

') � Key Idea Identifying Congruent Figures

Tvvo figures are congruent when corresponding angles and corresponding sides are congruent.

Triangle ABC is congruent to Triangle DEF.

6ABC= 6DEF

44 Chapter 2 Transformations '4 Multi-Lo.nguage Glossary at BigideasMaH,ifcom

EXAMPLE

EXAMPLE

�Clcl }' Exercises 8, 9,

and 12

Which square is congruent to Square A?

Square A Square 8 Square C

8 9

·□· ·□·8 9

Each square has four right angles. So, corresponding angles are congruent. Check to see if corresponding sides are congruent.

Square A and Square B

Each side length of Square A is 8, and each side length of Square B is 9. So, corresponding sides are not congruent.

Square A and Square C

Each side length of Square A and Square C is 8. So, corresponding sides are congruent.

::• So, Square C is congruent to Square A.

Trapezoids ABCD and JKLM are congruent.

a. What is the lengthofsideJM?

Side JM correspondsto side AD.

::• So, the length of side]M is 10 feet.

b. What is the perimeter of JKLM?

The perimeter of ABCD is 10 + 8 + 6 + 8 = 32 feet. Because thetrapezoids are congruent, their corresponding sides are congruent.

::• So, the perimeter of]K

LM is also 32 feet.

-, Qn Your Own

2. Which square in Example 2 is congruentto Square D?

3. In Example 3, which angle of JKLM correspondsto L C? What is the length of side K]?

Square D

Section 2.1 Congruent Figures

9

9

45

Key Vocabulary '4 transformation,

p. 50

image, p. 50

translation, p. 50

EXAMPLE

� You're i1.e_ad ·YExercises 4-9

A' is read "A prime." Use prime symbols when naming an image.

A-A'

B --- B'

c-c

A transformation changes a figure into another figure. The new figure is called the image.

A translation is a transformation in which a figure Qslides but does not turn. Every point of the figure moves the same distance and in the same direction.

Slide

Tell whether the blue figure is a translation of the red figure .

a.

...----\J-----.\J

The red figure slides to form the blue figure.

b- □□ The red figure turns to form the blue figure.

Q

;:• So, the blue figure is a translation of the red figure.

:=· So, the blue figure is not a translation of the red figure.

� On Your Own Tell whether the blue figure is a translation of the red figure. Explain.

') �· Id J J!'ey , ea

..___I___,/ \..,____\

Translations in the Coordinate Plane

Words To translate a figure a units horizontaDy and b units vertically in a coordinate plane, add a to the x-coordinates and b to the y-coordinates of the vertices.Positive values of a and b represent translations up and right. Negative values of a and b represent translations dovvn and left.

Algebra (x, y) - (x + a, y + b)

y

In a translation, the original figure and its image are congruent.

50 Chapter 2 Transformations .. Multi-Language Glossary at BigidecisMaJlc'om

b

bb

EXAMPLE

Translate the red triangle 3 units right and 3 units down. What are the

coordinates of the image?

�.o.i,y__'t".ou'ro nQ.

d �

Exercises 10 and 11

EXAMPLE

Move each vertex 3 units right and 3 units down.

Connect the vertices. Label as A', B', and C'.

;!· The coordinates of the image areA'(l, -2), B'(5, 2), and C'(4, -1).

I' On Your Own

4. WHAT IF? The red triangle is translated 4 units left and 2 unitsup. What are the coordinates of the image?

The vertices of a square areA(l, -2),B(3, -2), C(3, -4), and

D(l, -4). Draw the figure and its image after a translation 4 units

left and 6 units up.

Add -4 to each x-coordinate. So,

subtract 4 from each x-coordinate.

Add 6 to each

y-coordinate.A' B'

3

Vertices of A'B'C'D' E'f 2

>- �1 Vertices of ABCD

A(l, -2) (x- ,y-t-c} (1 - 4, -2 + 6) (3 - 4, -2 + 6) (3 - 4, -4 + 6) (1 - 4, -4 + 6)

A'(-3,4) B'(-1, 4) C'(-1,2) D'(-3,2)

-4 -3 -2 0 I 2 3 4 X

B(3, -2) C(3, -4) DO, -4)

�� You're&, d. • -0. }'

Exercises 12-15

:•· The figure and its image are shown at the above right.

t, On Your Own

I z I 3

I 4

A

D

5. The vertices of a triangle areA(-2, -2), B(O, 2), and C(3, O).

Draw the figure and its image after a translation 1 unitleft and 2 units up.

Section 2.2 Translations

8

C

51

Key Vocabulary '4 reflection, p. 56

line of reflection,

p. 56

EXAMPLE

�uJ:e.B.�d yExercises 4-9

Lesson Tutorials

BigideasMath

Line of reflection

A reflection, or flip, is a transformation in which a figure is reflected in a line called the line of reflection. A reflection creates a mirror image of the original figure. DILJ

t Flip

Tell whether the blue figure is a reflection of the red figure.

a. b.

The red figure can be flippedto form the blue figure.

If the red figure were flipped,

it would point to the left.

::• So, the blue figure is a reflection of the red figure.

::• So, the blue figure is not a reflection of the red figure.

i, On Your Own

Tell whether the blue figure is a reflection of the red figure. Explain.

1. 0

2. 3.

0 LJ Lj

J Key Idea Reflections in the Coordinate Plane

Words To reflect a figure in the x-axis, take the opposite of they-coordinate. To reflect a figure in the y-axis, take the opposite of the x-coordinate.

Algebra Reflection in x-axis: (x, y) � (x, -y) Reflection in y-axis: (x, y) � (-x, y) B'

In a reflection, the original figure and its image are congruent.

2 3 4 X

56 Chapter 2 Transformations ◄ Multi-Language Glossary at SigldeasMath�om

bb b

EXAMPLE 22

Take the opposite of the x-coordinate.

Vertices of PQRS

P(-2,5)

Q(-1, -1)

R(-4, 2)

S(-4, 4)

The vertices of a triangle are A(- I, I), B(-1, 3), and C(6, 3). Draw the figure and its reflection in the x-axis. What are the coordinates of the image?

Points B and C are 3 Point A is 1 unit t-t-=l::::l==!=-r-f5Fl units above the x-axis.

\. above the x-axis. 1 "-r-+=�+-+-+-1---,--t�;,...i

Plot point A' 1 unit below the x-axis. n���-1-_;:...+i_

6 X

+-�--+--'f'=;---1-� Plot points B' and C' 3 units below the x-axis. Connect the vertices.

::• The coordinates of the image are A'(-1, -1), B'(-1, -3), and C'(6, -3).

The vertices of a quadrilateral are P(-2, 5), Q(-1, -1), R(-4, 2), andS(-4, 4). Draw the figure and its reflection in the y-axis.

They-coordinate does not change.

6·

(-x, y) Vertices of P' Q' R'S'

(-(-2),5) P'(2, 5)

(-(-1), -1) Q'(l, -1)

(-(-4), 2) R'(4, 2)

(-(-4),4) 5'(4, 4)

::• The figure and its image are shown at the above right.

-, On Your Own

�cty Exercises 10-17

4. The vertices of a rectangle are A(-4, -3), B(-4, -1), C(-1, -1),

and D(-1, -3).

a. Draw the figure and its reflection in the x-axis.b. Draw the figure and its reflection in the y-axis.

c. Are the images in parts (a) and (b) congrnent? Explain.

Section 2.3 Reflections 57

Key Vocabulary .. rotation, p. 62

center of rotation, p. 62

angle of rotation, p. 62

EXAMPLE i]

When rotating figures, it may help to sketch the rotation in several steps, as shown in Example 1.

') l<ey Idea Rotations

A rotation, or t-urn, is a transformation in which a figure

Angle is rotated about a point called the center of rotation. The number of degrees a figure rotates is the angle

of rotation.

of rotation'--...

In a rotation, the original figure and its image are congruent.

You must rotate the puzzle piece 270° clockwise about point P to fit it into a puzzle. Which piece

fits in the puzzle as shown?

Center of rotation

@ ®

© -ii ®

Rotate the puzzle piece 270° clockwise about point P.

turn 270

::• So, the correct answer is © .

p

Turn

., On Your Own

62

�dy Exercises 10-12

1. Which piece is a 90° counterclockwise rotation about point P.

2. Is Choice D a rotation of the original puzzle piece? If not, wh tkind of transformation does the image show?

Chapter 2 Transformations i4 Multi-language Glossary at BigJdeasMathifcom

EXAMPLE

A 180° clockwiserotation and a 180°counterclockwise rotation have the same image. So, you do not need to specify direction when rotating a figure 180°.

EXAMPLE

Common Err.or .� Be sure to pay attention to whether a rotation is clockwise or counterclockwise.

�d.y Exercises 13-18

The vertices of a trapezoid are W(-4, 2},X(-3, 4), Y(-1, 4), and Z( -1, 2). Rotate the trapezoid 180° about the origin. What are the coordinates of the image?

x' ( Draw WXYZ.)-t:

.rI

$,_

-4 -3 -2

y y 4

L3

z \2 turn 180" -\ 1 y 0 \ .. 2 / V4x

\ ✓ w-2

Plot Z' so that segment OZ and segment OZ' are congruent and

/ form a 180° angle.

Use a similar method to l3

Z' j � plot points W', X', and Y'. I /

--4

I rY' ,X

' I Connect the vertices.

::• The coordinates ofthe image areW'(4, -2),X'(3, -4), Y'(l, -4), andZ'(l, -2).

The vertices of a triangle areJ(l, 2), K(4, 2), and L(l, -3). Rotate the triangle 90° counterclockwise about vertex L. What are the coordinates

of the image?

l) Draw JKL.J

Plot K' so that segment KL and V 3 .,v

segment K'L' are congruent and 2 J K

form a 90° angle. '"" ' I i_ I'\. K' ,

I I"'-. -2 0 z/3 4 X l Use a similar method to plot }- ]'.. , A I

point J'. Connect the vertices. c--.. � �, I turn 90·}' L4 L' L

I I

::• The coordinates of the image are]'(-4, -3), K'(-4, 0), and L'(l, -3).

_, On Your Own 3. A triangle has vertices Q(4, 5), R(4, 0), and 5(1, 0).

a. Rotate the triangle 90° counterclockwise about the origin.

b. Rotate the triangle 180° about vertex S.

c. Are the images in parts (a) and (b) congruent? Explain.

Section 2.4 Rotations 63

EXAMPLE

EXAMPLE

t---J---f-t--+- 4

3

l--�---+--1--- 2

The vertices of a rectangle areA(-3, -3), B(l, -3), C(l, -5), and D(-3, -5). Rotate the rectangle 90° clockwise about the origin, and then reflect it in the y-axis. What are the coordinates of the image1

D'

C ... Draw ABCD and �

rotate it 90 clockwise. '--r-::::

-4

i--. N.

D

A'

2 1

i----{t 8'

-

-2

I I

I 4

y A" O"l

'

Reflect the rotated. J1 2 4 X figure in the Yiaxis.

\ 8" C"

B

C

.

::• The coordinates of the image are A"(3, 3), B"(3, -1), C" (5, -1)

and D" (5, 3).

The image of a translation, reflection, or rotation is congruent to the original figure. So, two figures are congruent when one can be obtain from the other by a sequence of translations, reflections, and rotatio s.

The red figure is congruent to the blue figure. Describe a sequen e of transformations in which the blue figure is the image of the red �gure. You can turn the red figure 90° so that it has the same orientation as the blue figure. so, begin with a rotation.

After rotating, you need to slide the figure up.

::• So, one possible sequence of transformations is a 90° counterclockwise rotation about the origin followed by a translation 4 units up.

Ii, On Your Own 4. The vertices of a triangle are P(-1, 2), Q(-1, 0), and R(2, 0).

Rotate the triangle 180° about vertexR, and then reflect it in the x-axis. What are the coordinates of the image?

5. In Example 5, describe a different sequence of transformatiotin which the blue figure is the image of the red figure.

64 Chapter 2 Transformations I

b

'

Progress Check BigldeasMath

Tell whether the two figures are congruent. Explain your reasoning. (Section 2.1)

1. 2. 9 18

,o 12 9

18

16 12

Tell whether the blue figure is a translation of the red figure. (Section 2.2)

3.

Tell whether the blue figure is a reflection of the red figure. (Section 2.3)

5. 6.

DO X The red figure is congruent to the blue figure. Describe two different sequences of

transformations in which the blue figure is the image of the red figure. (Section 2.4)

7. I 1-4

I'\.. 3

V N� V I l

-4 -3 -2 lo I 2 3 4 X

8. II I.Y

i3

. 2 I.

--4 -3 -2 0 1 2 3 4 X

-2

I 3

I I I 4

2

I I I

3

I 4

9. AIRPLANE Describe a translation of the airplane

from point A to point B. (Section 2.2) A

.Y

I

X

/ r �� --- "'>)

( �'.F '>J V a✓

I X

10. MINIGOLF You hit the golf ball along the red path sothat its image will be a reflection in the y-axis. Does

the golf ball land in the hole? Explain. (Section 2.3)

Sections 2.1-2.4 Quiz 69

bb

b b

b b

Key Vocabulary '4

similar figures, p. 72

The symbol ~ means is similar to.

When writing a similarity statement, make sure to list the vertices of the figures in the correct order.

EXAMPLE

�dy Exercises 4-7

;) l<ey ldea Similar Figures

�-� Lesson Tutorials ',¥ SigideasMath com

Figures that have the same shape but not necessarily the same size are

called similadigures.

D�F

Triangle ABC is similar to Triangle DEF.

Words Two figures are similar when

• corresponding side lengths are proportional and• corresponding angles are congruent.

Symbols Side Lengths Angles Figures

AB BC AC LA=LD 6ABC- 6DEJ' -=-=-Df EF DF

LB=LE

LC=LF

Which rectangle is similar to Rectangle A?

Rectangle A Rectangle B Rectangle C

1, !2 12 6 4

6

Each figure is a rectangle. So, corresponding angles are congruent.

Check to see if corresponding side lengths are proportional.

Rectangle A and Rectangle B

Length of A = � = 1Width of A �I

--

Length ofB 6 WidthofB 2

Rectangle A and Rectangle C

Length of A _ 6 _ 3 Width of A 3 ----

Length ofC 4 2 Width ofC 2

::• So, Rectangle C is similar to Rectangle A.

if On Your Own

Not proportional

Proportional

1. Rectangle D is 3 units long and 1 unit wide. \l\fhich rectangle is

similar to Rectangle D?

72 Chapter 2 Transformations ◄ Multi-Language Glossary at BigideasMcith�om

EXAMPLE

�-•'l'.ou ',:e Read --- :y

Exercises 8-11

EXAMPLE

The triangles are similar. Find x.

Because the triangles are similar, corresponding side lengths are proportional. So, \.VTite and solve a proportion to find x.

6 8

9 X

6x = 72

X = 12

Write a proportion.

Cross Products Property

Divide each side by 6.

::• So, xis 12 meters.

� On Your Own The figures are similar. Find x.

2.__.--1x �

6 ft

3. ,.i __ J 7crQX

12 cm

An artist draws a replica of a painting that is 12 in. on the Berlin Wall. The painting includes a

red trapezoid. The shorter base of the similar

trapezoid in the replica is 3. 75 inches. What 15 in. is the height h of the trapezoid in the replica?

Because the trapezoids are similar, corresponding side lengths are proportional. So, write and solve a proportion to find h.

Painting

3.75 h

15 12

12 • 3-75 = 12 • l!:._15 12

3=h

Write a proportion.

Multiplication Property of Equality

Simplify.

h

3.75 in. 0 Replica

::• So, the height of the trapezoid in the replica is 3 inches.

(ii On Your Own 4. WHAT IF? The longer base in the replica is 4.5 inches. What is

the length of the longer base in the painting?

Section 2.S Similar Figures 73

78

EXAMPLE

r) l<ey ldea Perimeters of Similar Figures

·when two figures are similar, theratio of their perimeters is equal tothe ratio of their correspondingside lengths.

Perimeter of AABC AB BC AC

Perimeter of L!.DEF DE EF DF

Find the ratio (red to blue) of the perimeters of the similar rectangles.

6

Perimeter of red rectangle _ _± _ �Perimeter of blue rectangle 6 3

:,. The ratio of the perimeters is�-•• 3

i, On Your Own

1. The height of Figure A is 9 feet. The height of a similar Figure B is15 feet. What is the ratio of the perimeter of A to the perimeter of B?

") Key Idea Areas of Similar Figures

When two figures are similar, the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

Area of /\ABC= (1-lB)2 = (RC)2 = (AC)2

Area of 6 DEF DE EF OF

Chapter 2 Transformations

EXAMPLE

�� You're Re. d Q ¥

Exercises 4-7

EXAMPLE

18 yd

! 10�

Area = 200 yd2

Perimeter = 60 yd

Find the ratio (red to blue) of the areas

of the similar triangles.

Area of red triangle _ ( 6 )2Area of blue triangle 10

::• The ratio of the areas is�. 25

(i On Your Own 2. The base of Triangle Pis 8 meters. The base of a similar

Triangle Q is 7 meters. What is the ratio of the area of Pto the area of Q?

A swimming pool is similar in shape to a volleyball court. Find the

perimeter P and the area A of the pool.

The rectangular pool and the court are similar. So, use the ratio of corresponding side lengths to write and solve proportions to find the perimeter and the area of the pool.

Perimeter

Perimeter of court Width of courtPerimeter of pool Width of pool

60 10P 18

1080 = lOP

108 = P

Area

Area of court = (Width of comt )2

Area of pool Width of pool 200 = (

10)2

A 18

200 100A 324

64,800 = lOOA

648 =A

::• So, the perimeter of the pool is 108 yards, and the area is 648 square yards.

" On Y'our Own

3. WHAT IF? The width of the pool is 16 yards. Find the perimeter Pand the area A of the pool.

Section 2.6 Perimeters and Areas of Similar Figures 79

b

EXAMPLE

Key Vocabulary '4 dilation, p. 84

center of dilation,

p. 84

scale factor, p. 84

�dy Exercises 7-12

A dilation is a transformation in which a figure is made larger or smaller with respect to a point called the center of dilation. Center of

dilation

�

Tell whether the blue figure is a dilation of the red figure.

a. b.

t>

�

Lines connecting corresponding vertices meet at a point.

The figures have the same size and shape. The red figure slides to form the blue figure.

;:• So, the blue figure is not a dilation of the red figure. It is a translation.

::• So, the blue figure is a dilation of the red figure.

i, On Your Own

Tell whether the blue figure is a dilation of the red figure. Explain.

'·Oo 2.

□□ In a dilation, the original figure and its image are similar. The ratio of the side lengths of the image to the corresponding side lengths of the original figure is the scale factor of the dilation.

• :J l<ey l!deaDilations in the Coordinate Plane

Words To dilate a figure vvith respect to theorigin, multiply the coordinates of each vertex by the scale factor k.

Algebra (x, y) -. (kx, ky)

• When k > l, the dilation is an enlargement.

B'

C'

0 1 2 3 4 5 6 7.r

• When k > O and k < l, the dilation is a reduction.

84 Chapter 2 Transformations .. Multi-1.Q.nguage Glossary at BigideasMath�m

bbb

b

bb

,

EXAMPLE

Multiply each x- and y-coordinate by the

scale factor 3.

You can check your answer by drawing a line from the origin through each vertex of the original figure. The vertices of the image should lie on these lines.

EXAMPLE

Multiply each x- and y-coordinate by the

scale factor 0.5.

� XQ,u;ce Bga.dy Exercises 13-18

Draw the image of Triangle ABC after a dilation with a scale factor of 3.

Identify the type of dilation.

Vertices of .... Vertices of

ABC (3x, 3y)

A'B'C'

A{l, 3) (3 • 1, 3 • 3) A'(3, 9)

8(2, 3) (3 • 2, 3 • 3) B' (6, 9)

C(2, 1) (3 • 2, 3 • 1) C'(6,3)

::• The image is shown at the right. The dilation is an enlargement because the scale factor is greater than 1.

y 8' 9

8

7-

6

5-

2-

I

0 i 2 3 4 5 6 X ' ....__._._

Draw the image of Rectangle WXYZ after a dilation with a scale factor of 0.5. Identify the type of dilation.

Vertices of (O.Sx, O.Sy)

Vertices of WXYZ W'X'Y'Z'

W(-4, -6) (0.5 • (-4), 0.5 • (-6)) W(-2, -3)

X(-4, 8) (0.5 • (-4), 0.5 • 8) X'(-2,4) X 10-

Y(4, 8) (0.5 • 4, 0.5 • 8) Y'(2, 4) X' Y'

Z{4, -0) (0.5 • 4, 0.5 • (-6)) 2'(2, -3) 2-

-6 0

-

::• The image is shown at the right. The dilation is a reduction because the scale factor is greater than 0 and less than 1.

- VV:'--Z'

}s I

-, On Your Own

3. WHAT IF? Triangle ABC in Example 2 is dilated by a scalefactor of 2. What are the coordinates of the image?

4. WHAT IF? Rectangle vVXYZ in Example 3 is dilated by a scalefactor of.!.. vVhat are the coordinates of the image?

4

Ir

6 X

.......... -

z

-

Section 2.7 Dilations 85

86

EXAMPLE

The vertices of a trapezoid areA(-2, -1), B(-1, 1), C(O, 1), and D(O, -1). Dilate the trapezoid with respect to the origin using a scale

factor of 2. Then translate it 6 units right and 2 units up. What are the

coordinates of the image?

Draw ABCD. Then dilate it

with respect to the origin using a scale factor of 2.

Translate the dilated

figure 6 units right and 2 units up.

::• The coordinates of the image areA"(2, 0), B"(4, 4), C"(6, 4), and D"(6, 0).

The image of a translation, reflection, or rotation is congruent to the original figure, and the image of a dilation is similar to the original figure. So, tvvo figures are similar when one can be obtained from the other by a sequence of translations, reflections, rotations, and dilations.

EXAMPLE IB

0 1 2 3 4567.r

-2

L3+--+--.......... f---+--+-+---+-.......

14 ____ -+---+----

Ls

The red figure is similar to the blue figure. Describe a sequence of

transformations in which the blue figure is the image of the red figure.

From the graph, you can see that the blue figure is one-half the size of the red figure. So, begin with a dilation with respect to the origin using a scale factor of�-

After dilating, you need to flip the figure in the x-axis.

::• So, one possible sequence of transformations is a dilation with respect to the origin using a scale factor of.!.

2

followed by a reflection in the x-axis.

y - 3

- 2 I

0

-2

L3

--4

-5

I /;\

I I 1 2 4 5 6 7 X

,-,�

'I,

J I

1, v-"' -

i, On Your Own

Now..Y.ou'ro n_ -�dy

Exercises 23-28

5. In Example 4, use a scale factor of 3 in the dilation.Then rotate the figure 180

° about the image of vertex C. What are the coordinates of the image?

6. In Example 5, can you reflect the red figure first, and thenperform the dilation to obtain the blue figure? Explain.

Chapter 2 Transformations

b

b

90

™� Progress Check '.¥

BigideasMath com

1. Tell whether the two rectanglesare similar. Explain yourreasoning. (Section 2.5) 4m� 10m

The figures are similar. Find x. (Sectinn 2.5)

2. 3.

)(

22

Sm

8

14

20 m

X

The two figures are similar. Find the ratios (red to blue) of the perimeters and of the areas. (Section 2.6)

4. \�__,\ \___ ____,\ 8

5.

12

Tell whether the blue figure is a dilation of the red figure (Secrio11 2. 7)

6.0 0 7.

8. SCREENS The TV screen is similar to the ___ 20 in.12 in. computer screen. What is the area of

the TV screen? (Section 2.6)

9. GEOMETRY The vertices of a rectangle areA(2, 4), B(5, 4), C(5, -1), and D(2, -1).

Dilate the rectangle with respect to the origin using a scale factor of½· Then translate it 4 units left and 3 units down. What are the coordinates of the image? (Section 2. 7)

Area= 108 in.2

10. TENNIS COURT The tennis courts for singles and doubles matches aredifferent sizes. Are the courts similar? Explain. (Section 2.5)

T 27 ft

1

Chapter 2

Singles Doubles

I 36 ft

1 78 ft

Transformations

78 ft

b

b

b

b