Lesson 29 Introduction Graph Points in the Coordinate PlaneIntroduction 290 ©Curriculum Associates, LLC Copying is not permitted. Use What You Know Lesson 29 Gr aph Points in the

Introduction

©Curriculum Associates, LLC Copying is not permitted.290

Use What You Know

Lesson 29 Graph Points in the Coordinate Plane

Lesson 29Graph Points in the Coordinate Plane

a. What ordered pair represents Ring Toss?

b. What ordered pair represents Face Painting?

c. Describe one way to move from Ring Toss to Face Painting by first moving to the right.

d. Now describe a different path to get from Ring Toss to Face Painting.

The coordinate plane at the right shows the layout at a country fair. Some of the booths are labeled. Meg is at Ring Toss. She wants to go to Face Painting. Suppose Meg can only walk along the grid lines. Describe two different paths she can take.

In Lesson 28, you learned about the coordinate plane. Now you will use the coordinate plane to solve problems. Take a look at this problem.

x

y

1

1

2

3

4

5

O 2 3 4 5

SnackStand

Ring Toss

Book Sale

Face Painting

5.G.A.2

©Curriculum Associates, LLC Copying is not permitted. 291Lesson 29 Graph Points in the Coordinate Plane

Find Out More

On the previous page you used the coordinate plane to help you describe how to move between points. But you can do this without using the coordinate plane. You can use ordered pairs to describe how to move between points.

Use the ordered pairs (1, 1) and (2, 3) to describe how to move between the points. To describe the horizontal move, look at the change in the x-coordinates.

(1, 1)Ring Toss

(2, 3)Face Painting

2 2 1 5 1

Since 2 is to the right of 1 on the x-axis, the move is 1 unit to the right.

To describe the vertical move, look at the change in the y-coordinates.

(1, 1)Ring Toss

(2, 3)Face Painting

3 2 1 5 2

Since 3 is above 1 on the y–axis, the move is 2 units up.

You can describe the move from point (1, 1) to point (2, 3) as 1 unit right and 2 units up.

Reflect1 Pick two other points on the coordinate plane on the previous page. Use the

coordinates of the points to describe a path from one point to the other.

x

y

1

1

2

3

4

5

O 2 3 4 5

Ring Toss(1, 1)

Face Painting(2, 3)

Modeled and Guided Instruction

Learn About


Lesson 29


Relationships in the Coordinate Plane

Read the problem below. Then explore different ways to represent and use relationships between quantities to solve problems.

Gabe has $8. He goes to an arcade where each game costs $1. Use equations, a table, and the coordinate plane to represent the relationship between how many games Gabe plays and how much money he has left. How many games can Gabe play if he wants to have exactly $2 when he leaves the arcade?

Model It You can use equations to represent the relationship between the quantities in the problem.

Gabe starts with $8. Each game costs $1.

$8 2 ($1 3 number of games) 5 dollars left

$8 2 ($1 3 1) 5 $7 left

$8 2 ($1 3 2) 5 $6 left

$8 2 ($1 3 3) 5 $5 left

$8 2 ($1 3 4) 5 $4 left

$8 2 ($1 3 5) 5 $3 left

$8 2 ($1 3 6) 5 $2 left

Model It You can use a table to model the relationship between the quantities.The table shows how much money Gabe has left after playing different numbers of games.

Number of Games Played 0 1 2 3 4 5 6

Amount of Money Left ($) 8 7 6 5 4 3 2


Connect It Now you will solve the problem from the previous page by representing the relationship between the quantities using the coordinate plane.

2 What quantity in the problem stays the same?

What two quantities change?

3 Look at the coordinate plane. What quantity is represented on the x-axis?

What quantity is represented on the y-axis?

4 How much money does Gabe have after he plays 0 games? Complete the ordered pair.

(0 games, $ )

Plot the point in the coordinate plane.

5 Complete these ordered pairs, where x is games played and y is dollars left.

(1, ), (2, )

(3, ), (4, )

(5, ), (6, )

Plot each ordered pair in the coordinate plane.

6 How many games can Gabe play and have exactly $2 when he leaves? Which ordered

pair shows that?

7 How can you use a graph to represent relationships between two sets of numbers?

Try It Use what you just learned about representing relationships between two quantities using the coordinate plane to solve this problem. Show your work on a separate sheet of paper.

8 Suppose that the games at the arcade cost $2 each instead of $1. Write ordered pairs to represent the amounts of money left after playing different numbers of games. Use an “X” to plot each point on the coordinate plane above. How many of these games can Gabe play and have exactly $2 left when he leaves the arcade?

x

y

1

12345678

O 2 3 4 5 6 7 8Games Played

Mo

ney

Lef

t ($)

Modeled and Guided Instruction

Learn About


Lesson 29

Solving Problems on a Coordinate Plane


Read the problem below. Then explore different ways of using the coordinate plane to solve a problem.

Mrs. Sautter writes the following ordered pairs on the board: M(2, 1), A(2, 5), T(5, 5), and H(5, 1). The point represented by each ordered pair is a vertex of a rectangle. She lists the vertices in order to name the figure “rectangle MATH.” What is the perimeter of rectangle MATH?

Picture It You can picture the rectangle on a coordinate plane.Plot the points for the vertices of the rectangle. Connect the points to draw the sides of the rectangle. Then shade the rectangle.

x

y

1

1

2

3

4

5

O 2 3 4 5

A T

HM

To find the perimeter, count the number of units on each side to find the side lengths.

Model It You can find the perimeter of a rectangle with a formula.

<

<

ww

P 5 2, 1 2w or P 5 2 3 (, 1 w)


Connect It Now you will solve the problem from the previous page using your understanding of distance between two points on a number line.

9 What are the ordered pairs for points A and T?

Which are different, the x-coordinates or the y-coordinates?

Write an expression to find the distance between the points A and T.

What is the length of ··· AT ? units

10 Consider how you found the length of ··· AT above.

What is the length of ··· MA ? units

Explain how you found this length.

11 What is the perimeter of the rectangle? units

Explain how you found the perimeter.

12 How can you find the vertical distance between two points on a coordinate plane?

13 How can you find the horizontal distance between two points on a coordinate plane?

Try It Use what you just learned about finding the distance between two points on a number line to solve these problems.

14 What is the vertical distance between (3, 8) and (3, 4)?

15 What is the horizontal distance between (4, 2) and (4, 5)?

Guided Practice

Practice


Lesson 29



Example

Pair/ShareExplain how to use the graph to find how many chores Jaina must complete to earn $4.

Pair/ShareWhat shape could have the 4 points as vertices? Draw the shape on the coordinate plane.

Do parallel lines ever intersect?

The labels on the axes tell me what the numbers mean.

16 Plot the points (4, 4), (8, 4), (3, 1), and (7, 1) on the coordinate plane. Use the points to draw two parallel, horizontal segments. Label the endpoints of one segment A and B. Label the endpoints of the other segment C and D. What is the distance between points A and B? What is the distance between points C and D?

x

y

1

123456789

10

O 2 3 4 5 6 7 8 9 10

Solution

The graph shows how Jaina’s parents determine her weekly allowance. What is the meaning of (3, 5)?

Look at how you can use the graph to solve this problem.

The x-axisislabeled“Chores Completed.”Thex-coordinate in (3, 5) is 3. The y-axis is labeled “WeeklyAllowance.” The y-coordinate in (3, 5) is 5.

Solution

Study the example below. Then solve problems 16–18.

If Jaina completes 3 chores, she will earn $5.

x

y

1

123456

O 2 3 4 5 6W

eekl

yA

llow

ance

Chores Completed


Pair/ShareDoes Maya’s answer make sense?

Pair/ShareSuppose the x-coordinates for points G and H each increase by 1. What kind of shape would this be? What is the area of the shape?

The formula for the area of a rectangle is A = ø 3 w.

What is the ordered pair for the starting point?

17 What is the area of rectangle EFGH shown on the coordinate plane?

x

y

1

1234567

O 2 3 4 5 6 7 8 9 10

H

G

E

F

Show your work.

Solution

18 Mr. Palmer uses the coordinate plane to design his bulletin board.

He moves Rules 2 units right and 3 units down. What ordered pair represents the new location of Rules? Circle the letter of the correct answer.

A (5, 3)

B (1, 9)

C (1, 3)

D (5, 9)

Maya chose C as the correct answer. How did she get that answer?

x

y

1

1234567

O 2 3 4 5 6 7 8 9 10

Calendar

RulesTrivia

Independent Practice

Practice


Lesson 29



Solve the problems.

1 Look at triangle ABC.

x

y

1

1

2

3

4

5

6

7

8

O 2 3 4 5 6 7 8

B

C

A

What are the coordinates of points A, B, and C?

A A(1, 1), B(6, 3), C(4, 7)

B A(1, 1), B(3, 6), C(7, 4)

C A(0, 0), B(6, 3), C(4, 7)

D A(0, 0), B(3, 6), C(7, 4)

2 The coordinate plane below shows rhombus RHOM with lines of symmetry.

x

y

1

1

2

3

4

5

6

7

8

O 2 3 4 5 6 7 8

R

H

O

M

What is the horizontal distance between points R and O?

units

3 Plot the following three points on the coordinate plane below.

(2, 6) (7, 4) (4, 0)

x

y

1

1

2

3

4

5

6

7

8

O 2 3 4 5 6 7 8

Self Check


Go back and see what you can check off on the Self Check on page 283.

4 The coordinate plane shows the relationship between the amount of water in the bathtub and the amount of time the faucet has been turned on.

How many minutes must the faucet be turned on for the bathtub to hold 8 gallons of water?

A 16 minutes

B 8 minutes

C 4 minutes

D 2 minutes

5 Part A The area of rectangle RSTU is 20 square units. Draw rectangle RSTU on the coordinate plane below with one vertex at the origin.

x

y

1

1

2

3

4

5

6

7

8

O 2 3 4 5 6 7 8

Part B Write the ordered pairs for the points R, S, T, and U.

Part C How do you know that the area of rectangle RSTU is 20 square units?

x

y

1

12345678

O 2 3 4 5 6 7 8Time (minutes)

Wat

er (g

allo

ns)

Documents

Lesson 29 Introduction Graph Points in the Coordinate PlaneIntroduction 290 ©Curriculum Associates, LLC Copying is not permitted. Use What You Know Lesson 29 Gr aph Points in the