Ordered Pairs
Name
14.1
?
Geometry and Measurement—5.8.A, 5.8.B Also 5.8.C MATHEMATICAL PROCESSES 5.1.D, 5.1.E
Ordered Pairs
Essential Question
How can you identify and plot points in a coordinate grid?
Connect Locating a point on a coordinate grid is similar to describing directions using North-South and West-East. The horizontal number line on the grid is the x-axis. The vertical number line on the grid is the y-axis. Each point on the coordinate grid can be described by an ordered pair of numbers. The x-coordinate, the first number in the ordered pair, is the horizontal location, or the distance the point is from 0 in the direction of the x-axis. The y-coordinate, the second number in the ordered pair, is the vertical location, or the distance the point is from 0 in the direction of the y-axis. (x, y) x-coordinate
y-coordinate
The x-axis and the y-axis intersect at the point (0, 0), called the origin.
Unlock Unlock the the Problem Problem
Locate the point for which you want to write an ordered pair. Look below at the x-axis to identify the point’s horizontal distance from 0, which is its x-coordinate. Look to the left at the y-axis to identify the point’s vertical distance from 0, which is its y-coordinate.
So, the ordered pair for the arena is (3, 2) and the ordered pair for the aquarium
© Houghton Mifflin Harcourt Publishing Company
is (_ , _).
10 9 8 7 6 5 4 3 2 1
N W
0
E S
y-axis
Write the ordered pairs for the locations of the arena and the aquarium.
aquarium arena
1 2 3 4 5 6 7 8 9 10 x-axis
• Describe the path you would take to get from the origin to the aquarium, using horizontal, then vertical movements.
Module 14
511
Example Use the graph. A point in a coordinate grid can be labeled with an ordered pair, a letter, or both.
then up _ units.
10 9 8 7 6 5 4 3 2 1
Plot and label the point.
0
From the origin, move right 5 units and then up 7 units. Plot and label the point.
B Plot the point (8, 0) and label it S. From the origin, move right _ units and
y-axis
A Plot the point (5, 7) and label it J.
J (5, 7)
1 2 3 4 5 6 7 8 9 10 x-axis
Share Share and and Show Show Use Coordinate Grid A to write an ordered pair for the given point.
3. E __
4. F __
Plot and label the points in Coordinate Grid A. 5. M (0, 9)
6. H (8, 6)
7. K (10, 4)
8. T (4, 5)
9. W (5, 10)
10. R (1, 3)
10 9 8 7 6 5 4 3 2 1 0
Math Talk Mathematical Processes
Describe how you plotted point M in the coordinate grid.
512
E B F C
D 1 2 3 4 5 6 7 8 9 10 x-axis © Houghton Mifflin Harcourt Publishing Company
2. D __
y-axis
1. C __
Coordinate Grid A
Name
Problem Problem Solving Solving 11.
Write Math Write directions for plotting a point to represent the ordered pair (4, 6).
12.
If the y-coordinate for a point is zero, on which axis will the point lie? Explain.
Problem Problem Solving Solving Nathan and his friends are planning a trip to New York City. Use the map for 13–15. Each unit represents 1 city block. What’s the Error? Nathan says that Madison Square Garden is located at (0, 3) on the map. Is his ordered pair correct? Explain.
y-axis
13.
14. Use Graphs The Empire State Building is located 5 blocks
right and 1 block up from (0, 0). Write the ordered pair for this location. Plot and label a point for the Empire State Building.
© Houghton Mifflin Harcourt Publishing Company
15.
10 9 8 7 6 5 4 3 2 1 0
Bryant Park NY Public Library B Madison Square Garden 1 2 3 4 5 6 7 8 9 10 x-axis
Multi-Step Paulo walks from point B to Bryant Park. Raul walks from point B to Madison Square Garden. If they only walk along the grid lines, who walks farther? Explain.
Module 14 • Lesson 1
513
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble completely to show your answer. Use the map for 16–17.
American city. In the evening, the bats fly out from under the Congress Avenue Bridge. Which ordered pair shows the Congress Avenue Bridge?
A
(6, 6)
B
(6, 0)
C
(0, 6)
D
(0, 0)
y-axis
16. Austin has the largest bat colony of any North
State 10 Capitol 9 Governor’s 8 Mansion 7 6 Austin History Center 5 O.Henry 4 Museum Austin 3 Children’s 2 Museum Congress Avenue 1 Bridge 0
1 2 3 4 5 6 7 8 9 10
x-axis 17. You are standing very close to the O. Henry Museum.
Where might you be standing?
A
(3, 9)
C
(9, 2)
B
(2, 9)
D
(0, 10)
18. Multi-Step Look at the map. Today you went
A
J and K
B
J and M
C
K and L
D
K and M
10 9 8 7 6 5 4 3 2 1
y-axis
shopping at (0, 4) and had lunch at (8, 2). Which locations did you visit?
0
L
J M K 1 2 3 4 5 6 7 8 9 10
x-axis
19. Point R is 6 units to the right and 1 unit up from the origin.
What ordered pair describes point R?
514
A
(1, 6)
C
(6, 1)
B
(6, 0)
D
(1, 1)
© Houghton Mifflin Harcourt Publishing Company
TEXAS Test Prep
Geometry and Measurement—5.8.A, 5.8.B Also 5.8.C MATHEMATICAL PROCESSES 5.1.D, 5.1.E
H o mewo rk and Practice
14.1
Name
Ordered Pairs
Use Coordinate Grid M to write an ordered pair for the given point. 2. O _
3. P _
4. Q _
10 9 8 7 6 5 P 4 3 2 1
Plot and label the points in Coordinate Grid M. 5. R(2, 8)
6. S(6, 0)
7. T(8, 7)
8. U(10, 8)
Q
y-axis
1. N _
Coordinate Grid M
0 9. Is the ordered pair (4, 5) the same as the ordered pair (5, 4)? Explain.
O N 1 2 3 4 5 6 7 8 9 10 x-axis
Problem Problem Solving Solving The Alvarez family is spending the afternoon at the outdoor shopping center. Use the map for 10–11. Each unit represents 1 block. 10. The toy store is located 1 block right and 8 blocks
11. As Alma leaves the shoe store, it begins to rain.
© Houghton Mifflin Harcourt Publishing Company
She runs to the closest store. How many blocks is it to the closest store? Explain.
10 9 8 7 6 5 4 3 2 1
y-axis
up from (0, 0). Write the ordered pair for this location. Plot and label a point for the toy store.
0
grocery store jewelry store shoe store
1 2 3 4 5 6 7 8 9 10 x-axis
Module 14 • Lesson 1 515
TEXAS Test Prep
Lesson Lesson Check Check Fill in the bubble completely to show your answer. 12. The instructions for plotting a point in the
13. If you start at the origin, which of the following
coordinate grid read, “Start at the origin. Move right 6 units and then up 3 units.” What is the ordered pair for the point?
A
(6, 9)
B
(6, 3)
C
(3, 6)
D
(5, 2)
shows how to plot the point (2,5) in the coordinate grid?
A
Move up 5 units and then up 2 units.
B
Move right 2 units and then right 5 units.
C
Move right 2 units and then up 5 units.
D
Move right 5 units and then up 2 units.
Use the map of the garden center for 14–15. 14. Which ordered pair shows the location of
(0, 8)
B
(8, 0)
C
(8, 8)
D
(0, 0)
15. Which type of plants would you find at (9, 1)?
A
perennials
B
succulents
C
roses
D
herbs
0
B
(0, 7) and (6, 1)
C
(7, 0) and (1, 6)
D
(6, 1) and (7, 0)
y-axis
correct ordered pairs for points A and B? (1, 6) and (0, 7)
herbs
1 2 3 4 5 6 7 8 9 10
10 9 8 C 7 B 6 5 4 3 2 1 0
D A
1 2 3 4 5 6 7 8 9 10
x-axis 516
roses
x-axis
16. Multi-Step Look at the map. Which are the
A
10 9 8 annuals 7 perennials 6 5 4 succulents 3 2 1
© Houghton Mifflin Harcourt Publishing Company
A
y-axis
the annuals?
14.1
?
Geometry and Measurement—5.8.A, 5.8.B Also 5.8.C MATHEMATICAL PROCESSES 5.1.D, 5.1.E
Ordered Pairs
Essential Question
How can you identify and plot points in a coordinate grid?
Connect Locating a point on a coordinate grid is similar to describing directions using North-South and West-East. The horizontal number line on the grid is the x-axis. The vertical number line on the grid is the y-axis. Each point on the coordinate grid can be described by an ordered pair of numbers. The x-coordinate, the first number in the ordered pair, is the horizontal location, or the distance the point is from 0 in the direction of the x-axis. The y-coordinate, the second number in the ordered pair, is the vertical location, or the distance the point is from 0 in the direction of the y-axis. (x, y) x-coordinate
y-coordinate
The x-axis and the y-axis intersect at the point (0, 0), called the origin.
Unlock Unlock the the Problem Problem
Locate the point for which you want to write an ordered pair. Look below at the x-axis to identify the point’s horizontal distance from 0, which is its x-coordinate. Look to the left at the y-axis to identify the point’s vertical distance from 0, which is its y-coordinate.
So, the ordered pair for the arena is (3, 2) and the ordered pair for the aquarium
© Houghton Mifflin Harcourt Publishing Company
is (_ , _).
10 9 8 7 6 5 4 3 2 1
N W
0
E S
y-axis
Write the ordered pairs for the locations of the arena and the aquarium.
aquarium arena
1 2 3 4 5 6 7 8 9 10 x-axis
• Describe the path you would take to get from the origin to the aquarium, using horizontal, then vertical movements.
Module 14
511
Example Use the graph. A point in a coordinate grid can be labeled with an ordered pair, a letter, or both.
then up _ units.
10 9 8 7 6 5 4 3 2 1
Plot and label the point.
0
From the origin, move right 5 units and then up 7 units. Plot and label the point.
B Plot the point (8, 0) and label it S. From the origin, move right _ units and
y-axis
A Plot the point (5, 7) and label it J.
J (5, 7)
1 2 3 4 5 6 7 8 9 10 x-axis
Share Share and and Show Show Use Coordinate Grid A to write an ordered pair for the given point.
3. E __
4. F __
Plot and label the points in Coordinate Grid A. 5. M (0, 9)
6. H (8, 6)
7. K (10, 4)
8. T (4, 5)
9. W (5, 10)
10. R (1, 3)
10 9 8 7 6 5 4 3 2 1 0
Math Talk Mathematical Processes
Describe how you plotted point M in the coordinate grid.
512
E B F C
D 1 2 3 4 5 6 7 8 9 10 x-axis © Houghton Mifflin Harcourt Publishing Company
2. D __
y-axis
1. C __
Coordinate Grid A
Name
Problem Problem Solving Solving 11.
Write Math Write directions for plotting a point to represent the ordered pair (4, 6).
12.
If the y-coordinate for a point is zero, on which axis will the point lie? Explain.
Problem Problem Solving Solving Nathan and his friends are planning a trip to New York City. Use the map for 13–15. Each unit represents 1 city block. What’s the Error? Nathan says that Madison Square Garden is located at (0, 3) on the map. Is his ordered pair correct? Explain.
y-axis
13.
14. Use Graphs The Empire State Building is located 5 blocks
right and 1 block up from (0, 0). Write the ordered pair for this location. Plot and label a point for the Empire State Building.
© Houghton Mifflin Harcourt Publishing Company
15.
10 9 8 7 6 5 4 3 2 1 0
Bryant Park NY Public Library B Madison Square Garden 1 2 3 4 5 6 7 8 9 10 x-axis
Multi-Step Paulo walks from point B to Bryant Park. Raul walks from point B to Madison Square Garden. If they only walk along the grid lines, who walks farther? Explain.
Module 14 • Lesson 1
513
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble completely to show your answer. Use the map for 16–17.
American city. In the evening, the bats fly out from under the Congress Avenue Bridge. Which ordered pair shows the Congress Avenue Bridge?
A
(6, 6)
B
(6, 0)
C
(0, 6)
D
(0, 0)
y-axis
16. Austin has the largest bat colony of any North
State 10 Capitol 9 Governor’s 8 Mansion 7 6 Austin History Center 5 O.Henry 4 Museum Austin 3 Children’s 2 Museum Congress Avenue 1 Bridge 0
1 2 3 4 5 6 7 8 9 10
x-axis 17. You are standing very close to the O. Henry Museum.
Where might you be standing?
A
(3, 9)
C
(9, 2)
B
(2, 9)
D
(0, 10)
18. Multi-Step Look at the map. Today you went
A
J and K
B
J and M
C
K and L
D
K and M
10 9 8 7 6 5 4 3 2 1
y-axis
shopping at (0, 4) and had lunch at (8, 2). Which locations did you visit?
0
L
J M K 1 2 3 4 5 6 7 8 9 10
x-axis
19. Point R is 6 units to the right and 1 unit up from the origin.
What ordered pair describes point R?
514
A
(1, 6)
C
(6, 1)
B
(6, 0)
D
(1, 1)
© Houghton Mifflin Harcourt Publishing Company
TEXAS Test Prep
Geometry and Measurement—5.8.A, 5.8.B Also 5.8.C MATHEMATICAL PROCESSES 5.1.D, 5.1.E
H o mewo rk and Practice
14.1
Name
Ordered Pairs
Use Coordinate Grid M to write an ordered pair for the given point. 2. O _
3. P _
4. Q _
10 9 8 7 6 5 P 4 3 2 1
Plot and label the points in Coordinate Grid M. 5. R(2, 8)
6. S(6, 0)
7. T(8, 7)
8. U(10, 8)
Q
y-axis
1. N _
Coordinate Grid M
0 9. Is the ordered pair (4, 5) the same as the ordered pair (5, 4)? Explain.
O N 1 2 3 4 5 6 7 8 9 10 x-axis
Problem Problem Solving Solving The Alvarez family is spending the afternoon at the outdoor shopping center. Use the map for 10–11. Each unit represents 1 block. 10. The toy store is located 1 block right and 8 blocks
11. As Alma leaves the shoe store, it begins to rain.
© Houghton Mifflin Harcourt Publishing Company
She runs to the closest store. How many blocks is it to the closest store? Explain.
10 9 8 7 6 5 4 3 2 1
y-axis
up from (0, 0). Write the ordered pair for this location. Plot and label a point for the toy store.
0
grocery store jewelry store shoe store
1 2 3 4 5 6 7 8 9 10 x-axis
Module 14 • Lesson 1 515
TEXAS Test Prep
Lesson Lesson Check Check Fill in the bubble completely to show your answer. 12. The instructions for plotting a point in the
13. If you start at the origin, which of the following
coordinate grid read, “Start at the origin. Move right 6 units and then up 3 units.” What is the ordered pair for the point?
A
(6, 9)
B
(6, 3)
C
(3, 6)
D
(5, 2)
shows how to plot the point (2,5) in the coordinate grid?
A
Move up 5 units and then up 2 units.
B
Move right 2 units and then right 5 units.
C
Move right 2 units and then up 5 units.
D
Move right 5 units and then up 2 units.
Use the map of the garden center for 14–15. 14. Which ordered pair shows the location of
(0, 8)
B
(8, 0)
C
(8, 8)
D
(0, 0)
15. Which type of plants would you find at (9, 1)?
A
perennials
B
succulents
C
roses
D
herbs
0
B
(0, 7) and (6, 1)
C
(7, 0) and (1, 6)
D
(6, 1) and (7, 0)
y-axis
correct ordered pairs for points A and B? (1, 6) and (0, 7)
herbs
1 2 3 4 5 6 7 8 9 10
10 9 8 C 7 B 6 5 4 3 2 1 0
D A
1 2 3 4 5 6 7 8 9 10
x-axis 516
roses
x-axis
16. Multi-Step Look at the map. Which are the
A
10 9 8 annuals 7 perennials 6 5 4 succulents 3 2 1
© Houghton Mifflin Harcourt Publishing Company
A
y-axis
the annuals?
