lesson 7 homework practice distance on the coordinate plane

Distance on the Coordinate Plane

Related Topics: Lesson Plans and Worksheets for Grade 6 Lesson Plans and Worksheets for all Grades More Lessons for Grade 6 Common Core For Grade 6

Videos and solutions to help Grade 6 students learn how compute the length of horizontal and vertical line segments on the coordinate plane.

New York State Common Core Math Grade 6, Module 3, Lesson 18

Worksheets for Grade 6

Lesson 18 Student Outcomes

Students compute the length of horizontal and vertical line segments with integer coordinates for endpoints in the coordinate plane by counting the number of units between end points and using absolute value.

Opening Exercise

Four friends are touring on motorcycles. They come to an intersection of two roads ;the road they are on continues straight, and the other is perpendicular to it. The sign at the intersection shows the distances to several towns. Draw a map/diagram of the roads and use it and the information on the sign to answer the following questions:

What is the distance between Albertsville and Dewey Falls? What is the distance between Blossville and Cheyenne? On the coordinate plane, what represents the intersection of the two roads?

Example 1: The Distance Between Points on an Axis

What is the distance between (-4, 0) and (5, 0)?

What do the ordered pairs have in common and what does that mean about their location in the coordinate plane? How did we find the distance between two numbers on the number line? Use the same method to find the distance between (-4, 0) and (5, 0).

Example 2: The Length of a Line Segment on an Axis

What is the length of the line segment with endpoints (0, -6) and (0, 11)?

What do the ordered pairs of the endpoints have in common and what does that mean about the line segment’s location in the coordinate plane?

Find the length of the line segment described by finding the distance between its endpoints (0, -6) and (0, 11)?

Find the length of the line segment by finding the distance between its endpoints (-3, 3) and (-3, -5)

• Find the lengths of the line segments whose endpoints are given below. Explain how you determined that the line segments are horizontal or vertical. a) (-3, 4), (-3, 9) b) (2, -2), (-8, -2) c) (-6, -6), (-6, 1) d) (-9, 3), (-4, 4) e) (0,-11), (0, 8)

Lesson Summary

To find the distance between points that lie on the same horizontal line or on the same vertical line, we can use the same strategy that we used to find the distance between points on the number line.

Lesson 18 Distance in the Coordinate Plane.

Lesson 18 Exit Ticket

Determine whether each given pair of endpoints lies on the same horizontal or vertical line. If so, find the length of the line segment that joins the pair of points. If not, explain how you know the points are not on the same horizontal or vertical line. a. (0, -2) and (0, 9) b. (11, 4) and (2, 11) c. (3, -8) and (3, -1) d. (-4, -4) and (5, -4)

Problem Set

• Find the length of the line segment with end points (7,2) and (-4,2), and explain how you arrived at your solution.
• Sarah and Jamal were learning partners in math class and were working independently. They each started at the point (-2,5) and moved 3 units vertically in the plane. Each student arrived at a different end point. How is this possible? Explain and list the two different end points.
• The length of a line segment is 13 units. One end point of the line segment is (-3,7). Find four points that could be the other end points of the line segment.

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38.4: Distances on a Coordinate Plane

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Let's explore distance on the coordinate plane.

Exercise \(\PageIndex{1}\): Coordinate Patterns

Plot points in your assigned quadrant and label them with their coordinates.

Exercise \(\PageIndex{2}\): Signs of Numbers in Coordinates

• Write the coordinates of each point.
• Answer these questions for each pair of points.
• How are the coordinates the same? How are they different?
• How far away are they from the y-axis? To the left or to the right of it?
• How far away are they from the x-axis? Above or below it?
• \(A\) and \(B\)
• \(B\) and \(D\)
• \(A\) and \(D\)

Pause here for a class discussion.

• Point \(F\) has the same coordinates as point \(C\), except its \(y\)-coordinate has the opposite sign.
• Plot point \(F\) on the coordinate plane and label it with its coordinates.
• How far away are \(F\) and \(C\) from the \(x\)-axis?
• What is the distance between \(F\) and \(C\)?
• Plot point \(G\) on the coordinate plane and label it with its coordinates.
• How far away are \(G\) and \(E\) from the \(y\)-axis?
• What is the distance between and ?
• Point \(H\) has the same coordinates as point \(B\), except both of its coordinates have the opposite signs. In which quadrant is point \(H\)?

Exercise \(\PageIndex{3}\): Finding Distances on a Coordinate Plane

• Label each point with its coordinates.
• Point \(B\) and \(C\)
• Point \(D\) and \(B\)
• Point \(D\) and \(E\)
• Which of the points are 5 units from \((-1.5,-3)\)?
• Which of the points are 2 units from \((0.5,-4.5)\)?
• Plot a point that is both 2.5 units from \(A\) and 9 units from \(E\). Label that point \(F\) and write down its coordinates.

Are you ready for more?

Priya says, “There are exactly four points that are 3 units away from \((-5,0)\).” Lin says, “I think there are a whole bunch of points that are 3 units away from \((-5,0)\).”

Do you agree with either of them? Explain your reasoning.

The points \(A=(5,2), B=(-5,2), C=(-5,-2),\) and \(D=(5,-2)\) are shown in the plane. Notice that they all have almost the same coordinates, except the signs are different. They are all the same distance from each axis but are in different quadrants.

Notice that the vertical distance between points \(A\) and \(D\) is 4 units, because point \(A\) is 2 units above the horizontal axis and point \(D\) is 2 units below the horizontal axis. The horizontal distance between points \(A\) and \(B\) is 10 units, because point \(B\) is 5 units to the left of the vertical axis and point \(A\) is 5 units to the right of the vertical axis.

We can always tell which quadrant a point is located in by the signs of its coordinates.

In general:

• If two points have \(x\)-coordinates that are opposites (like 5 and -5), they are the same distance away from the vertical axis, but one is to the left and the other to the right.
• If two points have \(y\)-coordinates that are opposites (like 2 and -2), they are the same distance away from the horizontal axis, but one is above and the other below.

When two points have the same value for the first or second coordinate, we can find the distance between them by subtracting the coordinates that are different. For example, consider \((1,3)\) and \((5,3)\):

They have the same \(y\)-coordinate. If we subtract the \(x\)-coordinates, we get \(5-1=4\). These points are 4 units apart.

Glossary Entries

Definition: Quadrant

The coordinate plane is divided into 4 regions called quadrants. The quadrants are numbered using Roman numerals, starting in the top right corner.

Exercise \(\PageIndex{4}\)

Here are 4 points on a coordinate plane.

• Plot a point that is 3 units from point \(K\). Label it \(P\).
• Plot a point that is 2 units from point \(M\). Label it \(W\).

Exercise \(\PageIndex{5}\)

Each set of points are connected to form a line segment. What is the length of each?

• \(A=(3,5)\) and \(B=(3,6)\)
• \(C=(-2,-3)\) and \(D=(-2,-6)\)
• \(E=(-3,1)\) and \(F=(-3,-1)\)

Exercise \(\PageIndex{6}\)

On the coordinate plane, plot four points that are each 3 units away from point \(P=(-2,-1)\). Write the coordinates of each point.

Exercise \(\PageIndex{7}\)

Noah’s recipe for sparkling orange juice uses 4 liters of orange juice and 5 liters of soda water.

• Noah prepares large batches of sparkling orange juice for school parties. He usually knows the total number of liters, \(t\), that he needs to prepare. Write an equation that shows how Noah can find \(s\), the number of liters of soda water, if he knows \(t\).
• Sometimes the school purchases a certain number, \(j\), of liters of orange juice and Noah needs to figure out how much sparkling orange juice he can make. Write an equation that Noah can use to find \(t\) if he knows \(j\).

(From Unit 6.4.1)

Exercise \(\PageIndex{8}\)

For a suitcase to be checked on a flight (instead of carried by hand), it can weigh at most 50 pounds. Andre’s suitcase weighs 23 kilograms. Can Andre check his suitcase? Explain or show your reasoning. (Note: 10 kilograms \(\approx\) 22 pounds)

(From Unit 3.2.3)

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Eureka Math Grade 5 Module 6 Lesson 7 Answer Key

Engage ny eureka math 5th grade module 6 lesson 7 answer key, eureka math grade 5 module 6 lesson 7 problem set answer key.

a. Use a straightedge to draw a line connecting these points. b. Write a rule showing the relationship between the x- and y-coordinates of points on the line. c. Name 2 other points that are on this line. Answer:

a. Use a straightedge to draw a line connecting these points. b. Write a rule showing the relationship between the x- and y-coordinates. c. Name 2 other points that are on this line. Answer: a.

b. A rule showing the relationship between the x- and y-coordinates of points on the line is Double the x coordinate is the y coordinates . c. The 2 other points that are on this line are (\(\frac{3}{4}\), 1 \(\frac{3}{4}\)) and (1\(\frac{1}{4}\), 2\(\frac{1}{2}\))

Eureka Math Grade 5 Module 6 Lesson 7 Exit Ticket Answer Key

Question 1. Use a straightedge to draw a line connecting these points. Answer:

Question 2. Write a rule to show the relationship between the x- and y-coordinates for points on the line. Answer: A rule to show the relationship between the x- and y-coordinates for points on the line is the difference between x and y coordinate is 4

Question 3. Name two other points that are also on this line. __________ __________ Answer: The two other points that are also on this line are (1, 5) and (4, 8)

Eureka Math Grade 5 Module 6 Lesson 7 Homework Answer Key

a. Use a straightedge to draw a line connecting these points. b. Write a rule showing the relationship between the x- and y-coordinates of points on this line. c. Name two other points that are also on this line. Answer: a.

b. A rule showing the relationship between the x- and y-coordinates of points on this line is The difference                between x coordinate and y coordinate is 2 c . The two other points that are also on this line are (3, 1) and ( 4, 2) .

a. Use a straightedge to draw a line connecting these points. b. Write a rule showing the relationship between the x- and y-coordinates for points on the line. c. Name two other points that are also on this line. _____________ _____________ Answer: a.

b. A rule showing the relationship between the x- and y-coordinates for points on the line is Increasing from 0 to (\(\frac{1}{2}\) , (\(\frac{1}{2}\) to 1 and 1 to 2 increasing by double the x coordinate . c. The two other points that are also on this line are

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Distance on the Coordinate Plane

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• Grade 6 Mathematics Module 5, Topic B, Lesson 7: Student Version
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Finding Distance on the Coordinate Plane Practice Worksheets (Classwork & HW)

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Finding Distance on the Coordinate Plane Practice Worksheets (Classwork & Homework):

This set of classwork and homework assignments will help your students learn how to find the distance between 2 points on the coordinate plane. These practice worksheets require students to find the distance between 2 points using either the Pythagorean Theorem or the Distance Formula. The instructions ask students to write their answers in simplified radical form. These practice worksheets include a 2-page classwork assignment and a 2-page homework assignment for a total of 4 pages of practice!

Each assignment is 2 pages long with 15 problems per assignment. The first 6 problems provide a graph, but the next 8 problems do not provide graphs. The last question of each assignment asks students to find the perimeter of a square or rectangle. These assignments are a wonderful opportunity for your students to practice simplifying radicals. I recommend allowing your students to use calculators, but a calculator is not necessary.

This set of practice worksheets comes with 4 pages of practice (1 classwork assignment and 1 homework assignment), answer keys, and a PowerPoint file containing pictures of the worksheets and keys. The worksheets in the PowerPoint are NOT editable. When you purchase this set of practice worksheets, you will receive a pdf containing the worksheets and answer keys, and you will receive a PowerPoint file. Before purchasing this product, please review the preview file closely to make sure that the problem types are appropriate for your students.

If you would like to purchase these practice worksheets with guided notes, you may also like:

Finding Distance on the Coordinate Plane Lesson Materials

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Chapter 3, Lesson 7: Geometry: Distance on the Coordinate Plane

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Chapter 3, Lesson 7: Geometry: Distance on the Coordinate Plane

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