Topic 16 Coordinate Geometrymrsevansclass.weebly.com/.../topic_16_coordinate_geometry_stude… · Topic 16 Coordinate Geometry _____ Name ... 5. D 6. C 7. E 8. L ... B Division C

Topic 16

Coordinate Geometry

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Test Date

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Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5

Topic 16

Vocabulary Cards

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coordinate grid

coordinate grid

A grid that makes it easy to locate points

on a plane by using an ordered pair of numbers.

x-axis

x-axis

The horizontal axis in a graph or coordinate grid.

y-axis

y-axis

The vertical axis in a graph or coordinate grid.

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origin

ordered pair

x-coordinate

origin

The point at which the x-axis and the y-axis of a coordinate plane intersect. The origin

is represented by the ordered pair (0, 0).

ordered pair

A pair of numbers used to locate a point on a

coordinate grid.

x-coordinate

The first number in an ordered pair which names the distance

from the origin along the x-axis.

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y-coordinate

y-coordinate

The second number in an ordered pair which names the distance

from the origin along the y-axis.

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Daily Common Core Review16-1

1. �An�office�worker�made�10�telephone�calls�on�Monday.�He�made�3�calls�before�lunch.�Which�decimal�tells�the�fraction�of�the�calls�he�made�before�lunch?�

A 3.10

B 0.10

C 0.3

D 1.3

2. �Which�of�the�following�is�the�standard�form�of�104?�

A 10

B 100

C 1,000

D 10,000

3. �Ms.�Jones�drove�2,700�miles�in�9�weeks�for�her�job.�If�she�drove�the�same�distance�each�week,��how�many�miles�did�she�drive��in�one�week?

A 3,000�miles

B 300�miles

C 30�miles

D 3�miles

4. �Eight�friends�used�608�tickets�for�rides�at�the�amusement�park.�If�each�person�used�the�same�number�of�tickets,�how�many�tickets�did�each�person�use?�

5. �Nan�has�88�stickers�to�put�in�14�bags.�She�wants�to�put�the�same�number�of�stickers�in�each�bag�and�have�the�least�number�of�stickers�left�over.�

a �How�many�stickers�should�Nan�put�in�each�bag?

b �Will�Nan�have�any�stickers�left�over?�If�so,�how�many?�Explain�how�you�decided.

D 16•1

A

LH

I

F

EJC

G

BK

D

2 4 6 81 3 5 7 9 10

1110987654321

0

y

x

2 4 6 81 3 5 7 90

y

x

987654321

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Practice

16-1Ordered PairsName the point that is located by each ordered pair.

1. (9, 3) 2. (1, 0)

3. (7, 5) 4. (5, 7)

Write the ordered pair for each point.

5. D 6. C

7. E 8. L

Plot and label each point on the grid to the right.

9. M(3, 4) 10. Z(6, 5)

11. T(0, 9) 12. X(4, 4)

13. P(3, 0) 14. A(2, 8)

15. H(7, 7) 16. B(2, 9)

17. J(3, 7) 18. L(1, 6)

19. Which is the ordered pair for a point that is 7 units to the right of zero along the x-axis and 8 units above it?

A (8, 7) C (1, 7)

B (7, 8) D (1, 8)

20. Why are (4, 6) and (6, 4) not at the same point on a grid?

P 16•1

1 2 3 4 5

A

B

C

DE

FG

H54321

x

y

0

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Quick Check

16-1

Use the coordinate grid to answer Questions 1 through 3.

1. What is the ordered pair that names Point D?

A (5, 3)

B (2, 2)

C (1, 4)

D (3, 1)

2. Imagine a post office is at Point B and a grocery store is at Point D. Each unit is a city block. Which of the following explains how to get from the post office to the grocery store?

A Move 1 block east and 4 blocks south.

B Move 2 blocks east and 3 blocks south.

C Move 1 block east and 2 blocks south.

D Move 4 blocks east and 1 block south.

3. Writing to Explain Explain how to locate the coordinates for Point G on the coordinate grid.

Q 16•1

0 1 2 3 4 5 6 7 8 x

y

Henry

Max

Sal

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1. �Which�number�is�NOT�a�factor�of�36?�

A 3�

B 6

C 12

D 24

2. �Which�expression�has�the�same�value�as�103?

A 10�+�10�+�10

B 10�×�10�×�10

C 10�×�3

D ��10�___�3��

3. �Carla�has�600�oranges�to�pack�into�24�crates.�If�each�crate�holds�the�same�number�of�oranges,�how�many�oranges�are�in�each�crate?�

A 25

B 30

C 35

D 50

4. �Sandra�buys�6�shirts.�Each�shirt�costs�$17.�Which�is�the�best�operation�for�finding�the�total�cost�for�all�of�the�shirts?

A Subtraction

B Division

C Multiplication

D Substitution

For�5�and�6,�use�the�coordinate�grid.

5. �Lisa’s�house�is�4�units�right�of�Henry’s�house.�Write�the�ordered�pair�for�Lisa’s�house.�Graph�and�label�Lisa’s�house�on�the�grid.

6. �Josh’s�house�has�the�same�y-coordinate�as�Sal’s�house,�and�the�same�x-coordinate�as�Max’s�house.�Write�the�ordered�pair�for�Josh’s�house.�Explain�how�you�decided.

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2

0 2 4 6 8 10 12 14

4

6

8

10

12

14

x

y

2

0 2 4 6 8 10 12 14

4

6

8

10

12

14

x

y

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Practice

16-2Patterns and GraphingIn 1 and 2 create a data table from the points plotted on the graph.

3. Janice is 7 years older than Tam. Complete the table, and then graph this situation.

4. There are 4 cupcakes in every package. Complete the table, and then graph this situation.

5. Tickets to the River Dell Middle School concert cost $6 apiece. Complete the table, and then graph this situation.

6. A graph includes the ordered pair (2, 4). Write two different rules that would be possible for this graph. Explain how you found your answer.

Tam x (years)

Janicey (years)

2 9

4

6

8

x (number of packages)

y (number of cupcakes)

1 42345

x (tickets sold)

y (money received)

1 $62345

1. 2.

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0

8

Time (h)

Dis

tance

Tra

vele

d (

mi)

x

y

321

4

12

16

20

24

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Quick Check

16-2

3. WritingtoExplain A go-cart travels 8 miles an hour. Let x = the number of hours. Let y = the total number of miles. Make a table to show three x- and y-values that satisfy the rule. Graph the data. Explain your graph.

x y

1. What is the missing value in the table?

x y

2 6

4 12

6

8 24

A 16

B 18

C 20

D 22

2. What is the value of y when x = 6?

A 76

B 54

C 49

D 42

x y

1 7

2 14

3 21

4 28

5 35

6

7 49

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20 4 6 81 3 5 7

2

4

6

8

1

3

5

7

AC B

D

x

y

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1. �What�point�on�this�coordinate�grid�is�named�by�the�ordered�pair�(2,�3)?

A A

B B

C C

D D

2. Which�is�NOT�equivalent�to��1�__�2��?

A ��2�__�1��

B ��6�___�12

��

C 0.50

D ��50�____�100

��

3. Which�is�a�rule�for�y?

x 2 4 6 8

y 6 12 18 24

A y�is�x�divided�by�3

B y�is�x�plus�4

C y�is�x�plus�8

D y�is�3�times�x

4. �There�are�27�bones�in�each�of�your�hands�and�26�bones�in�each�of�your�feet.�How�many�bones�are�there�in�your�hands�and�feet�in�all?

5. �Six�friends�each�received�5�fruit�snacks.�Write�an�equation�to�find�the�total�number�of�fruit�snacks,�s.�Then�solve�to�find�s.�Explain�how�you�got�your�answer.

Equation:

s =

D 16•3

0 5 10

5

10

15

y1

y2

0 2 4 6 8 10 12 14 16 18

2

4

6

8

10

y1

y2

20 4 6 8

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1012141618

Dis

tanc

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iles)

Time (hours)x

y

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Practice

16-3More Patterns and GraphingFor 1 and 2, graph the corresponding coordinates of y1 and y2. Describe the relationship between the two sequences.

3. Dean is on a hike. The graph shows how far away he is from a camp site. How far away is he after 2 hours?

A 5 miles C 15 miles

B 10 miles D 20 miles

4. Ian gets $9 for each hour he works and $10 for each day he works. To find out how much he makes in a day, he made the equation y = 9x + 10x, where x is the number of hours he works. Explain why Ian’s equation will not tell him how much he makes in a day.

Day y1 y2

1 1 72 3 93 5 114 7 13

Week y1 y2

2 4 13 8 24 12 35 16 4

1.

2.

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5

10

15

20

0 5 10 15 20 y1

y2

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Quick Check

16-3

3. Writing to Explain Completethetablesbelow.Usethey-valuesfromeachofthetablestocreateanewsetofcoordinatedata.Graphthedataonacoordinateplaneandexplaintherelationshipbetweenthey1andy2values.

1. Whichorderedpairisasolutionforthesetofdata?

A (6,3)

B (8,5)

C (2,5)

D (4,11)

2. Whichtwoorderedpairswouldbeonthegraphforthecoordinateslistedinthetable?

A (6,26)and(15,19)

B (2,14)and(3,19)

C (5,29)and(7,31)

D (4,8)and(6,10)

x y1 52 73 9

5 13

x y10 5411 5912 6413 6914 74

x y1

1 3

2 6

9

5

6 18

x y2

1 4

2 7

4 13

5 16

6

Q 16•3

20 4 6 81 3 5 7

2

4

6

8

1

3

5

7

x

y

W

X

Y

Z

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Use the coordinate grid to answer Questions 1 and 2.

1. Name the ordered pair for Point Z.

A (3, 8)

B (8, 3)

C (2, 5)

D (5, 2)

2. Which point is located at (8, 8)?

A Point W

B Point X

C Point Y

D None of the above

3. Sheree has 40 coins. Of them, 20 are quarters. What fraction of Sheree’s coins are quarters?

A 1 __ 2

B 1 __ 4

C 1 __ 6

D 1 ___ 20

4. Ned’s Pet Store has 618 fish in 6 tanks. There is an equal number of fish in each tank. How many fish are there in each tank?

5. Erin’s favorite number is 808.Jen’s favorite number is 303. Ian’s favorite number is the sum of Erin’s and Jen’s. Ronald’s favorite number is the sum of Ian’s and Erin’s. What is Ronald’s favorite number? Explain how you found your answer.

D 16•4

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Practice

16-4Graphing Number PatternsMark and John keep track of the number of laps they walk around the track each day for a 4-day period. Mark’s rule is “Add 2” and John’s rule is “Add 6.”

Day 0 Day 1 Day 2 Day 3 Day 4Mark 0 2 4 6 ■

John 0 6 12 ■ 24

1. Use Mark’s rule to find the missing value in his row of the table for Day 4.

2. Use John’s rule to find the missing value in his row of the table for Day 3.

3. Complete the table to write ordered pairs showing the number of laps Mark and John walked after each day.

4. Plot the ordered pairs and the line that represent the data.

2468

1012141618202224

21 43 6 75 80

y

x

John’s

Laps

Mark’s Laps

5. Writing to Explain Write a statement that compares the number of laps Mark and John walked each day.

6. Look for a Pattern If Mark and John continue to walk the same number of laps each day, how many laps will John have walked when Mark has walked 10 laps? How many laps will Mark have walked when John has walked 36 laps?

Mark’s Laps (x) John’s Laps (y)0 02 6

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y

x

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Quick Check

16-4

For 1 through 3, use the information and the table below.

Andrea and Sue keep track of the number of packages of stickers that they buy each day. Andrea’s’s rule is “Add 3” and Sue’s rule is “Add 6.”

Day 0 Day 1 Day 2 Day 3 Day 4Andrea 0 3 6 9 ■

Sue 0 6 12 18 ■

1. What is the missing value in Andrea’s row of the table for Day 4?

A 10

B 11

C 12

D 15

2. What is the missing value in Sue’s row of the table for Day 4?

A 27

B 24

C 21

D 19

3. Writing to Explain Look at the sticker data above.

a. Write the ordered pairs showing the number of packages of stickers Andrea and Sue bought each day.

b. Graph the ordered pairs.

c. Write a statement that compares the number of packages Andrea and Sue bought.

Q 16•4

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1. Which rule describes the relationship between x and y?

A x is 3 more than y.B x is 3 less than y.C x is increasing by 3.

D y is increasing by 3.

2. Jean-Claude earns $5.00 an hour working at an ice cream store. Each day he buys one pint of ice cream for $2. Which numerical expression shows the amount of money he takes home after working 6 hours and then buying the pint of ice cream?

A 5 3 6 1 2

B 2 3 6 1 5

C 5 3 (6 2 2)

D 5 3 6 2 2

3. y is 1 less than 2 times x. Which ordered pair fits this rule?

A (1, 1)

B (1, 2)

C (1, 3)

D (1, 4)

4. Complete the table of values for the following rule.

yis 4 less than x.

5. Create a table of values for the following rule.

yis 2 more than x.

x 0 3 8 10

y 3 6 11 13 x y

4

5

6

14

x y

D 16•5

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Practice

16-5Problem Solving: Work BackwardWork backward to find each starting position.

1. Starting ( x, y). 4 units (14, 20)

2 units (14, 22)

5 units (9, 22) Ending


3 units (8, 6)

1 unit (8, 7) Ending


4 units (9, 13)


4. Martha must finish her math quiz in 35 minutes. She knows that there are 10 multiple-choice questions and 5 word problems. If each word problem takes her exactly 3 minutes to complete, how much time can she spend on each multiple-choice question?

5. Kori arrived at school on time, at exactly 8:30 a.m. If it took him 15 minutes to walk to school, 10 minutes to eat breakfast, and 18 minutes to get ready, what time did he wake up this morning?

A 7:37 a.m. C 7:57 a.m.

B 7:47 a.m. D 8:07 a.m.

6. Jerry used his $100 gift certificate to go shopping. He bought pants for $25, a shirt for $15, and socks for $3. Then he bought a pair of shoes. Jerry still has $27 left. How much were the shoes that he bought? Explain how you know.

P 16•5

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Quick Check

16-5

Work backward to solve.

1. What is the starting position ( x, y)?

Starting ( x, y)

8 units (2, 4)

4 units (2, 8)


A (10, 4)

B (8, 4)

C (8, 6)

D (6, 2)

2. Lydia kept track of the number of yards she swam in 3 days. On the first day, she swam a certain number of yards. On the second day, she swam 1,750 yards. On the third day, she swam 2,000 yards. If she swam a total of 5,200 yards, how many yards did she swim on the first day?

A 2,250 yd

B 2,000 yd

C1,750 yd

D 1,450 yd

3. WritingtoExplain Todd walked to the post office from his house. If the post office has the position (6, 9) on a map and he walked the following directions and distances, at what point on the map is Todd’s house? Explain how you solved the problem.

Todd’sHouse ( x, y)

2 units (2, 4)

4 units (6, 4)

5 units (6, 9) PostOffice

Q 16•5

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Topic 16 Coordinate Geometrymrsevansclass.weebly.com/.../topic_16_coordinate_geometry_stude… · Topic 16 Coordinate Geometry _____ Name ... 5. D 6. C 7. E 8. L ... B Division C