Introduction ©Curriculum Associates, LLC Copying is not permitted. 284 Think It Through Lesson 28 Understand the Coordinate Plane Lesson 28 Understand the Coordinate Plane What is the coordinate plane? In the past, you have used a number line to represent a single quantity. A number line can be vertical or horizontal. When a horizontal number line and a vertical number line are lined up so that the 0s meet, a coordinate plane is formed. 0 1 2 4 3 Vertical Number Line 0 1 2 4 3 Horizontal Number Line Coordinate Plane x y 1 1 2 3 4 O 2 3 4 A coordinate plane is made up of two perpendicular number lines. The number lines meet at the zeros. That point is labeled with the letter O for origin. Coordinate Plane x y 1 1 2 3 4 5 O 2 3 4 5 y-axis Origin x-axis The horizontal number line is called the x-axis. The vertical number line is called the y-axis. The point where the x- and y-axes meet is the origin. Think How do we distinguish between the two number lines? Circle all of the numbers on the x-axis. Box all of the numbers on the y-axis. 5.G.A.1
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Introduction
©Curriculum Associates, LLC Copying is not permitted.284
Think It Through
Lesson 28 Understand the Coordinate Plane
Lesson 28Understand the Coordinate Plane
What is the coordinate plane?
In the past, you have used a number line to represent a single quantity. A number line can be vertical or horizontal.
When a horizontal number line and a vertical number line are lined up so that the 0s meet, a coordinate plane is formed.
0
1
2
4
3
Vertical Number Line
0 1 2 43
Horizontal Number Line
Coordinate Plane
x
y
1
1
2
3
4
O 2 3 4
A coordinate plane is made up of two perpendicular number lines. The number lines meet at the zeros. That point is labeled with the letter O for origin.
Coordinate Plane
x
y
1
1
2
3
4
5
O 2 3 4 5
y-axis
Origin x-axis
The horizontal number line is called the x-axis. The vertical number line is called the y-axis. The point where the x- and y-axes meet is the origin.
Think How do we distinguish between the two number lines?
Circle all of the numbers on the x-axis. Box all of the numbers on the y-axis.
5.G.A.1
©Curriculum Associates, LLC Copying is not permitted. 285Lesson 28 Understand the Coordinate Plane
An ordered pair is a pair of numbers that describes the location of a point in the coordinate plane. The first number is called the x-coordinate. The second number is called the y-coordinate.
x-coordinate y-coordinate
Ordered Pair(x, y)
The x-coordinate tells the distance from the origin along the x-axis. The y-coordinate tells the distance from the origin along the y-axis.
The origin is the point where the x-axis and the y-axis meet. Since the origin is 0 units along the x-axis and 0 units along the y-axis, the location is (0, 0).
Term Definition
coordinate plane a space formed by two perpendicular number lines called axes
x-axis the horizontal number line in the coordinate plane
y-axis the vertical number line in the coordinate plane
origin the point, (0, 0), where the x-axis and y-axis intersect
ordered paira pair of numbers that describes the location of a point in the coordinate plane
x-coordinate the first number in an ordered pair
y-coordinate the second number in an ordered pair
Reflect1 Think about how you have heard the word origin used outside of math. Why do you
think the point (0, 0) is called the origin?
Think How can you locate points on the coordinate plane?
An ordered pair is a pair of coordinates that always appear in the same order: first x, then y.x
y
1
1
2
3
4
5
O 2 3 4 5
(0, 0)
(4, 3)
Guided Instruction
Think About
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Lesson 28
Points on a Coordinate Plane
Lesson 28 Understand the Coordinate Plane
x
y
1
1
2
3
4
O 2 3 4A
C
D
B
2 Locate point D in the coordinate plane above. Start at the origin. How many units do you move along the x-axis to be lined up under point D? Write this as the first number in the ordered pair at the right.
3 The second number in an ordered pair is the y-coordinate. Start at the origin. How many units do you move along the y-axis to be lined up across from point D? Write this as the second number in the ordered pair above.
4 Locate point A in the coordinate plane above. Start at the origin. How many units do you move along the x-axis to be on point A? Start at the origin. How many units do you move along the y-axis to be lined up across from point A?
The ordered pair for point A is ( , ).
5 Locate point B in the coordinate plane above. Identify the ordered pair for point B.
( , )
6 Locate point C in the coordinate plane above. Identify the ordered pair for point C.
( , )
7 How did you determine the coordinates for points C and D?
Let’s Explore the Idea Ordered pairs represent the location of points on the coordinate plane. The ordered pair for the origin is (0, 0).
Ordered Pair for Point D
(x, y) ( , )
©Curriculum Associates, LLC Copying is not permitted. 287Lesson 28 Understand the Coordinate Plane
Let’s Talk About It Solve the problems below as a group.
Use the coordinate plane from the previous page. Now you will describe the points as movements from the origin.
8 Place your finger on the origin. Move right and then move up to point D. Use words
to describe how far to the right and how far up point D is from (0, 0).
How is the location of point D related to the ordered pair (2, 3)?
9 Start at (0, 0). Move to point A. How is your move related to the ordered pair (1, 0)?
10 Describe how you move from the origin to the point (0, 1). Move right units and move unit.
What letter represents this point on the coordinate plane?
11 The ordered pair (1, 1) tells you to start at the origin and move right unit(s) and
up unit(s). What letter names this point on the coordinate plane?
12 Plot a point at (3, 2) on the coordinate plane. Label this point “E.”
Try It Another Way Work with your group to show the coordinates for each point on the coordinate plane on the previous page.
13 Complete the table for each point on the coordinate plane.
Point A B C D E F
x 1 3 4
y 0 2 0
14 The table gives the location of point F. Plot and label point F in the coordinate plane.
Guided Practice
Connect
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Lesson 28
Lesson 28 Understand the Coordinate Plane
Ideas About Points on a Coordinate Plane
Talk through these problems as a class. Then write your answers below.
15 Show Look at the table below. Plot and label points M and N on the coordinate plane below. Then write ordered pairs for points M and N and describe how to move from (0, 0) to each point.
Point x y
M 1 4
N 5 2
x
y
1
123456
O 2 3 4 5 6
16 Analyze Irvin wrote the ordered pair (4, 3)
x
y
1
1
2
3
4
5
O 2 3 4 5
J
for the location of point J in the coordinate plane at the right. Explain why Irvin’s ordered pair is incorrect for point J.
17 Create Choose 3 points on the coordinate plane at the right and draw a triangle. Label the points with letters.
Below, write the letters and ordered pairs you used to draw your triangle.
x
y
1
1
2
3
4
5
O 2 3 4 5
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Independent Practice
Apply
Lesson 28
Lesson 28 Understand the Coordinate Plane
Ideas About Points on a Coordinate Plane
18 Put It Together Use what you have learned to complete this task.
Part A Use the coordinate plane below to complete the table.
AB
CD
x
y
1
123456789
10
O 2 3 4 5 6 7 8 9 10
Point x y
A
B
C
D
Part B Identify a pattern you see formed by the points in the coordinate plane above. Then, explain the pattern using the points in the table above.
Part C Plot 3 other points that follow this pattern. Label them with letters and write the ordered pair for each point below.
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