Lesson 14 - Store & Retrieve Data Anywhere · A music store is at point M on the coordinate plane...

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©Curriculum Associates, LLC Copying is not permitted. 139Lesson 14 The Coordinate Plane

Lesson 14

Name: The Coordinate Plane

Prerequisite: Graph Points

Study the example showing how to plot points on a coordinate grid. Then solve problems 1–11.

1 What ordered pair describes the origin?

2 What are the coordinates of point A?

x-coordinate: y-coordinate:

3 Along which axis do you count each number of units in order to plot point A?

3 units to the right: -axis 4 units up: -axis

4 Plot a new point at (4, 3) Label the point C

5 Zachary says that point C has the same location as point A because both points have the same coordinates Is Zachary right? Explain why or why not

2 41 3Ox

y

2

1

4

3

origin

A

Vocabularyx-coordinate a point’s

horizontal distance from

the origin along the

x-axis

y-coordinate a point’s

vertical distance from

the origin along the

y-axis

Example

The location of a point is named with an x-coordinate and a y-coordinate The coordinates are written as an ordered pair, (x-coordinate, y-coordinate) Follow these steps to plot point A at (3, 4)

• Start at the origin

• Move 3 units to the right

• Move 4 units up

• Label the point A

139139

(0, 0)

3 4

x y

No; Possible explanation: The x- and

y-coordinates for points A and C are reversed.

B

B

B

M

B

C

©Curriculum Associates, LLC Copying is not permitted.140 Lesson 14 The Coordinate Plane

Solve.

Use the coordinate plane at the right to solve problems 6–9.

6 Plot and label the following points

Q(5, 5) R(7, 3) S(2, 8)

7 Choose one point from problem 6 Complete the following statements to describe how you plotted the point

a. Start at ( , )

b. Move units to the right Move units up

c. Label the point

8 Plot points at (0, 3), (0, 1), and (0, 5) What is true about all points with an x-coordinate of 0?

9 Plot points at (2, 0), (4, 0), and (3, 0) What is true about all points with a y-coordinate of 0?

Use the coordinate plane at the right to solve problems 10–11.

10 Write ordered pairs for four points that you can plot on the coordinate plane Each ordered pair must have a y-coordinate that is 2 units less than its x-coordinate Plot the points

11 Describe a pattern for the points you plotted in problem 10

2 41 3 5 6 7Ox

y

2

1

4

3

5

6

7

8

2 41 3 5Ox

y

2

1

4

3

5

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M

M

M

M

C

M

Possible answer:

0 0

2 8

S

Possible answer: The points are all on the y-axis.

Possible answer: The points are all on the x-axis.

Possible answer: (2, 0), (3, 1), (4, 2), (5, 3)

Possible answer: The points can be connected with a straight line. Moving left to right

along the line, you can plot each point by counting 1 unit to the right and 1 unit up.

R

S

Q

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Unit 2 Th

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Name: Lesson 14

Graphing on the Coordinate Plane

Study the example showing how to graph on the coordinate plane. Then solve problems 1–7.

1 Which exhibit is located at point E on the coordinate plane?

2 What are the x- and the y-coordinates of point E?

3 How are the x-coordinate and the y-coordinate in an ordered pair related to the origin?

4 Complete the table below to describe the location of each exhibit

Exhibit Location from the Origin

Fossils

Birds

Planets

Energy

Example

The table shows the locations of exhibits at a science museum Graph each exhibit on the coordinate plane

Exhibit Fossils Birds Planets Energy

Coordinates (3, 2) (21, 23) (2, 22) (23, 1)

For each ordered pair in the table, start at the origin, move left or right according to the x-coordinate, and then move up or down according to the y-coordinate

21

1

21 3

22

212223

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x

y

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EF

P

B

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B

B

B

B

Energy

x-coordinate: 23, y-coordinate: 1

Possible answer: The x-coordinate is the number of units to the left or the right of the

origin. The y-coordinate is the number of units up or down from the origin.

1 unit left, 3 units down

2 units right, 2 units down

3 units right, 2 units up

3 units left, 1 unit up


Solve.

Use this information for problems 5–6.

You can use a coordinate plane to represent the locations of different activities at a summer camp The ordered pairs in the table show the location of each activity

Activity Canoeing Swimming Hiking Art Fishing

Coordinates (26, 5) (2, 22) (23, 23) (4, 6) (24, 0)

5 Graph each activity as a point on the coordinate plane Label each point with the fi rst letter of the activity

21

1

21 3 4 5 6

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23

24

25

26

212223242526

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5

6

2

x

y

O

6 Describe the location from the origin of each point in problem 5

7 What are the signs of the coordinates of a point in each of the four quadrants?

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Point C is 6 units left, 5 units up. Point S is 2 units right, 2 units down. Point H is 3 units

left, 3 units down. Point A is 4 units right, 6 units up. Point F is 4 units left.

Possible answer: Quadrant I: both coordinates are positive; Quadrant II: negative

x-coordinate, positive y-coordinate; Quadrant III: both coordinates are negative;

Quadrant IV: positive x-coordinate, negative y-coordinate.

M

M

M

S

AC

F

H

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Unit 2 Th

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Unit 2

Practice Lesson 14 The Coordinate Plane


Solve.

Use the information for problems 5–7.

The points L, M, and N are reflected across the y-axis to get the points F, G, and H on the coordinate plane at the right

5 List the coordinates of the points shown in the graph

Point L: ( ) Point F: ( )

Point M: ( ) Point G: ( )

Point N: ( ) Point H: ( )

6 How are the coordinates of each point and its refl ection the same? How are they diff erent?

7 How do the coordinates of a point compare with the coordinates of its refl ection across the y-axis?

8 Becky refl ects point Q at (25, 24) across the x-axis to get point Z What are the coordinates of point Z? Explain how you know

9 Kanika plots point A at (1, 22) Next she plots a refl ection of point A at point W Finally, Kanika plots a refl ection of point W at point T, which is located at (21, 2) Describe how Kanika could have refl ected each of the points to arrive at point T

21

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21 3 4 5 6

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212223242526

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The x-coordinates are opposites; the

y-coordinates are the same.

The x-coordinates have opposite signs, and the y-coordinates are the same.

(25, 4); The x-coordinates of a point and its reflection across the x-axis are the same,

but the y-coordinates have opposite signs.

Possible answer: The reflection of point A across the x-axis is point W at (1, 2). The

reflection of point W across the y-axis is point T at (21, 2).

B

B

M

M

C

2, 6 22, 6

23, 1

26, 3

3, 1

6, 3


Name: Lesson 14

Refl ect Points

Study the example problem showing how to reflect points across the x-axis. Then solve problems 1–9.

1 What points are the refl ections of points M, N, and K across the x-axis?

2 List the coordinates of the other points of rectangle LMNK and rectangle PQRS

Point M: ( ) Point Q: ( )

Point N: ( ) Point R: ( )

Point K: ( ) Point S: ( )

3 How are the coordinates of points M and Q, points N and R, and points K and S the same? How are they diff erent?

4 How do the coordinates of a point compare with the coordinates of its refl ection across the x-axis?

Example

Rectangle LMNK is reflected across the x-axis to get rectangle PQRS How do the coordinates of point L change when it is reflected across the x-axis?

The coordinates of point L are (2, 6) The reflection of point L across the x-axis is point P The coordinates of point P are (2, 26)

The x-coordinate of the reflection of point L is the same as point L, but the y-coordinate has the opposite sign

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1

21 3 4 5 6

22

23

24

25

26

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L K

M N

Q R

P S

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The reflection of point M is point Q. The reflection of point N is point R. The reflection of

point K is point S.

Each pair of points have the same x-coordinate and opposite y-coordinates.

B

B

B

2, 3 2, 23

6, 23

6, 26

6, 3

6, 6

The x-coordinates are the same, and the y-coordinates have opposite signs.

M

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Solving

Unit 2 Th

e Num

ber System U

nit 2Practice Lesson 14 The Coordinate Plane


Solve.

Use the situation below and the coordinate plane to solve problems 5–8.

A music store is at point M on the coordinate plane An electronics store is at point E, and a restaurant is located at point R Each unit represents 1 mile

5 What are two ways you can fi nd the distance between the electronics store and the music store?

6 What is the distance between the electronics store and the music store? Count units to fi nd the answer

7 Use absolute value to fi nd the distance between the music store and the electronics store

Show your work.

Solution:

8 Helen drove from the restaurant to the toy store, which is not shown on the map She made a right turn at the toy store and drove to the music store She drove a total distance of 12 miles What are the coordinates of the toy store?

9 Point A is located at (23, y), and point B is located at (26, y) How can you fi nd the distance between these points using absolute values?

21

1

21 3 4 5 6

22

23

24

25

26

212223242526

3

4

S(4, 5)R(24, 4)

E(24, 23)

M(1, 23)

C(4, 26)

5

6

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x

y

O

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I can count units or I can use absolute value to

find the distance.

5 miles

The distance to the electronics store from the y-axis is |24|. The distance to the music store from the y-axis is |1|.

|24| 1 |1| 5 4 1 1 5 5

The distance between the electronics store and the music store is 5 miles.

(1, 4)

You can find the distance between points with the same y-coordinate in the same

quadrant by subtracting the absolute values of the x-coordinates.

B

B

M

C

C


Name:

Distance Between Points

Study the example showing how to find the distance between points in different quadrants. Then solve problems 1–9.

1 What are the y-coordinates of the sports store and the clothing store?

2 What do |5| and |26| represent in the example?

3 What is the relationship between the distance of the sports store and the clothing store from the x-axis and the y-coordinate of each point?

4 Explain how to count units to check the answer

Example

The locations of different stores are shown on the map There is a sports store at point S and a clothing store at point C Each unit on the coordinate plane represents 1 mile How many miles is the clothing store from the sports store?

Notice that the stores have the same x-coordinates, but they are in different quadrants To find the distance between them, find the distances of both points from the x-axis and add them

|5| 1 |26| 5 5 1 6 5 11

The clothing store is 11 miles from the sports store

Lesson 14

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21 3 4 5 6

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S(4, 5)R(24, 4)

E(24, 23)

M(1, 23)

C(4, 26)

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6

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x

y

O

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sports store: 5, clothing store: 26

|5| is the distance of point S, or the sports store, from the x-axis. |26| is the distance of

point C, or the clothing store, from the x-axis.

The distance of the clothing store and the sports store from the x-axis is the absolute

value of the y-coordinate of each point.

B

B

M

Count the units between the points. There are 11 units from S to C, so the answer

is correct.

B

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Solving

Unit 2 Th

e Num

ber System

Unit 2

Practice Lesson 14 The Coordinate Plane


Solve.

3 Four points representing the corners of a square are D(24, 5), E(3, 5), F(3, 22), and G(24, 22) Graph and label the points on the coordinate plane

4 How could you move the square in problem 3 so that each corner point is a refl ection of another corner point across the x- and y-axes? Explain your answer and graph the new square

Show your work.

Solution:

How do you find the distance between points?

What do the coordinates of a point tell you about its location from the origin?

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21 3 4 5 6

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24

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Possible answer:

The side length of the square between points D and E is |24| 1 3 5 7 units.

For each corner point to be a reflection of

another corner across the x- and y-axes,

each point needs to be the same distance

from both axes: 7 ·· 2 5 3.5 units.

The square should have points at

D(23.5, 3.5), E(3.5, 3.5), F(3.5, 23.5),

and G(23.5, 23.5).

M

C

F

ED

G

F

ED

G


Name: Lesson 14

The Coordinate Plane

Solve the problems.

1 Which statements are true about the coordinate plane? Choose all that apply

A DKLM is reflected across the y-axis to get DRTS

B The x-coordinates of points K and R are the same

C The y-coordinates of points K and R have opposite signs

D The y-coordinates of points L and T are the same

Which axis are the triangles reflected across?

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x

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K

LM

T

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Overset

2 In the coordinate plane in problem 1, how can you fi nd the distance from point R to the x-axis? Choose all that apply

A Find the absolute value of the x-coordinate in (24, 25)

B Add the absolute values of the x- and y-coordinates

C Count the number of units down from the x-axis

D Find the absolute value of the y-coordinate in (24, 25)

Julio chose A as a correct answer How did he get that answer?

What are the x- and y-coordinates of point R?

147

M

M

Possible answer: He found the absolute value of the x-coordinate instead of

the absolute value of the y-coordinate of point R.

Lesson 14 - Store & Retrieve Data Anywhere · A music store is at point M on the coordinate plane...

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Transcript of Lesson 14 - Store & Retrieve Data Anywhere · A music store is at point M on the coordinate plane...