Problem Solving on the Coordinate Plane
Videos and solutions to help Grade 6 students learn how solve problems related to the distance between points that lie on the same horizontal or vertical line and the coordinate plane.
New York State Common Core Math Module 3, Grade 6, Lessons 19
Students use the coordinate plane to graph points, line segments and geometric shapes in the various quadrants and then use the absolute value to find the related distances.
Opening Exercise
In the coordinate plane, find the distance between the points using absolute value. Exercises
1. Locate and label (4, 5) and 4, –3 ) Draw the line segment between the endpoints given on the coordinate plane. How long is the line segment that you drew? Explain.
2. Draw a horizontal line segment starting at (4, -3) that has a length of units. What are the possible coordinates of the other endpoint of the line segment? (There is more than one answer.)
Which point do you choose to be the other endpoint of the horizontal line segment? Explain how and why you chose that point. Locate and label the point on the coordinate grid.
- Each of the vertices lies in a different quadrant.
- Its sides are either vertical or horizontal.
- The perimeter of the rectangle is 28 units.
Using absolute value, show how the lengths of the sides of your rectangle provide a perimeter of 28 units.
Lesson Summary
The length of a line segment on the coordinate plane can be determined by finding the distance between its endpoints.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.
High Impact Tutoring Built By Math Experts
Personalized standards-aligned one-on-one math tutoring for schools and districts
In order to access this I need to be confident with:
Coordinate plane
Here you will learn about a coordinate plane, including the general form of a coordinate plane, plotting coordinates on different axes, and determining the coordinates of a point.
Students will first learn about coordinate planes as part of the number system in 6th grade.
What is a coordinate plane?
A coordinate plane is formed when a vertical number line overlaps a horizontal number line, forming a 2 dimensional gridded surface. It can also be called a coordinate grid.
The horizontal number line is called the \textbf{x} -axis and the vertical number line is called the \textbf{y} -axis . They intersect at the origin , (0,0).
In a coordinate plane there are four quadrants. The values on the x and y axes are different in each quadrant :
Note, it is also common for the names of the quadrants to be written with Roman numerals (I, II, III, IV).
Each axis has a scale . The scale must increase in equal amounts , but the scale does not have to be the same for both axes.
For example,
Here, both the x -axis and | Here, the x -axis increases | Here, the x -axis increases |
Coordinates are used to determine location on the coordinate plane.
A coordinate is written as (x,y), where the value for the x -coordinate represents the horizontal position of the coordinate, the value for the y -coordinate represents the vertical position of the coordinate and they are enclosed with parentheses.
These can also be referred to as ordered pairs.
For example, the coordinate (3,5) has a horizontal position of 3, and a vertical position of 5.
Besides locating the position of a coordinate, you can also plot coordinates within all four quadrants.
To do this, determine the horizontal and vertical position of the coordinate on the axes, and follow these values until the two values meet.
Draw the point A \, (4,2).
To draw the point, locate 4 on the x -axis, and then 2 on the y -axis. Follow the straight lines from these points to the coordinate A \, (4,2).
Note, to give a coordinate a specific name, label it as a point by using a capital letter.
Repeating this process by plotting points B \, (-4,4), \, C \, (-5,-3), and D \, (1,-2)…
Note that coordinates can have decimal values. It is common to only see integer coordinates that lie on a grid line, however, you can also plot coordinates that have a decimal value, such as E \, (2.5, 3.5) and F \, (-3, 1.5).
These would lie within or on the edge of a grid square.
[FREE] Algebra Check for Understanding Quiz (Grade 6 to 8)
Use this quiz to check your grade 6 to 8 students’ understanding of algebra. 10+ questions with answers covering a range of 6th and 8th grade algebra topics to identify areas of strength and support!
Common Core State Standards
How does this relate to 6th grade math?
- Grade 6 – The Number System (6.NS.C.8) Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
How to plot on a coordinate plane
In order to plot on a coordinate plane:
Determine the horizontal position of the coordinate (the value of \textbf{x} ).
Determine the vertical position of the coordinate (the value of \textbf{y} ).
Follow the gridlines until the two values meet and draw a point.
Coordinate plane examples
Example 1: plot a coordinate.
Plot the coordinate A \, (-12, 4).
The x value is -12, so locate -12 on the x -axis. The scale is 1, so -12 is two gridlines after -10.
2 Determine the vertical position of the coordinate (the value of \textbf{y} ).
The y value is 4, so locate 4 on the y -axis. The scale is 1, so 4 is one gridline before 5.
3 Follow the gridlines until the two values meet and draw a point.
Following the gridlines…
This gives us the final solution.
Example 2: plot a coordinate
Plot the coordinate H \, (-5, -7).
The x value is -5, so locate -5 on the x -axis. The scale is 2, so -5 is between -4 and -6.
The y value is -7, so locate -7 on the y -axis. The scale is 2, so -7 is between -6 and -8.
Following between the gridlines…
Example 3: plot a coordinate on the x -axis
Plot the coordinate B \, (-2,0).
The x value is -2, so locate -2 on the x -axis.
The y value is 0, so locate 0 on the y -axis.
Example 4: plot a coordinate on the y -axis
Plot the coordinate C \, (0,0.4).
The x value is 0, so locate 0 on the x -axis.
The y value is 0.4, so locate 0.4 on the y -axis. The scale is 0.2, so 0.4 is two gridlines above 0.
Example 5: plotting two coordinates
Plot the coordinates R \left(3,- \, \cfrac{3}{2} \, \right) and Q \left(\cfrac{5}{2},- \, 5 \right).
Since there are two coordinates, plot each point one at a time.
The x value of the point R is 3, so locate 3 on the x -axis.
The y value of the point R is -\cfrac{3}{2} \, , so locate -\cfrac{3}{2} \, on the y -axis.
Since -\cfrac{3}{2}= -1 \, \cfrac{1}{2} \, , it is in between -1 and -2.
Following the gridlines (and between them)…
The point R is located here.
Repeat this process for the point Q \left(\cfrac{5}{2},- \, 5 \right).
Example 6: plotting coordinates in three quadrants
Plot the coordinates D \, (-1,-3), \, E \, (-1,5) , and F\, (3,-2) on the set of axes below.
Since there are three coordinates, plot each point one at a time.
The x value of the point D is -1, so locate -1 on the x -axis.
The y value of the point D is -3, so locate -3 on the y -axis.
The point D is located here.
Repeat this process for the point E…
Repeating the process for the point F…
Teaching tips for the coordinate plane
- Worksheets play an important role when students are learning to plot on a coordinate plane, but they are not the only option. There are digital coordinate planes available where students can easily change the scale and explore grids with very small or very large scales that would be harder to represent on paper. You can also utilize a tiled floor or wall to create a physical version of the coordinate plane within the classroom.
- Coordinate planes have so many real life uses, and students understand them best with repeated use. To make the repeated practice more engaging, give students the opportunity to create and use a coordinate plane to solve a real world problem. It could be physical, for example, using string and stakes to create a grid in the school garden for proper plant distances. Or using a program to code a video game that requires students to indicate the position of the characters and items in each frame of the game.
Easy mistakes to make
- Mixing up the values in the coordinate It is important to remember that the first number is x and represents the horizontal axis. The second number is y and represents the vertical axis. Confusing these, in most cases, will affect the location of the coordinate.
- Forgetting the values between the gridlines Each axis is created by a number line, which has infinite rational values on it. If a coordinate lies between gridlines, rather than on a gridline, a smaller ratio of the scale can be used to find the exact position. Continuing to use the original scale or guessing, will lead to an incorrect answer.
- Not using parentheses and a comma The parentheses and the comma are required when writing a coordinate. Coordinates can be incorrectly written as 3,2 without the parentheses, this is just a list of numbers; (3,2) is a coordinate.
Related coordinate plane lessons
- Interpreting graphs
- x and y axis
- Graph transformations
- Plot points on a graph
- Independent and dependent variables
Practice coordinate plane questions
1. What is the coordinate shown below?
The first value is along the x axis and the second value is along the y axis.
The x value of the coordinate is 10.
The y value of the coordinate is 5.
The coordinate is written as (10,5).
2. What is the coordinate shown below?
The coordinate is written as (-1.5,4).
3. Which diagram correctly shows the location of the point (2.5,4.5)?
This graph shows the coordinate (2.5,4.5).
4. Which diagram correctly shows the location of the point A \, (-3,-1)?
This graph shows the coordinate (-3,-1).
5. What is the coordinate shown below?
The scale for the x and y axes is 0.2.
This graph shows the coordinate (-1.2,1).
6. What is the coordinate shown below?
The scale for the x and y axes is 0.5.
This graph shows the coordinate (1,-2).
Coordinate plane FAQs
This is the same as a coordinate plane. This name refers to the French mathematician Rene Descartes who is credited with incorporating the use of the coordinate plane into mathematics.
Coordinate planes have many uses in the real world and come up extensively in upper level math topics like geometry, algebra, and statistics.
The next lessons are
- Types of graphs
- Graphing linear equations
- Rate of change
Still stuck?
At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.
Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.
Find out how we can help your students achieve success with our math tutoring programs .
[FREE] Common Core Practice Tests (Grades 3 to 6)
Prepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents.
40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!
Privacy Overview
You are using an outdated browser and it's not supported. Please upgrade your browser to improve your experience.
- LOGIN FOR PROGRAM PARTICIPANTS
- PROGRAM SUPPORT
Problem Solving With The Coordinate Plane
Description.
Develop coordinate system for the first quadrant of the coordinate plane, points, ordered pairs, patterns, lines , exploration of the coordinate plane in real world applications.
There may be cases when our downloadable resources contain hyperlinks to other websites. These hyperlinks lead to websites published or operated by third parties. UnboundEd and EngageNY are not responsible for the content, availability, or privacy policies of these websites.
- End-of-Module Assessment - Word Document
- Grade 5 Mathematics Module 6: Answer Keys
- Grade 5 Module 6: Full Module
- Grade 5 Module 6: Spanish - Zip Folder of PDF Files
- Grade 5 Module 6: Spanish - Zip Folder of Word Documents
- Show More ...
- Mid-Module Assessment - Word Document
- Module Overview - Word Document
- Topic A Lessons 1-6 - Zip File of Word Documents
- Topic B Lessons 7-12 - Zip File of Word Documents
- Topic C Lessons 13-17 - Zip File of Word Documents
- Topic D Lessons 18-20 - Zip File of Word Documents
- Topic E Lessons 21-25 - Zip File of Word Documents
- Topic F Lessons 26-34 - Zip File of Word Documents
- Show Less ...
Prerequisites
- CCSS Standard:
In This Module
- topic A: Coordinate Systems
- topic B: Patterns In The Coordinate Plane And Graphing Number Patterns From Rules
- topic C: Drawing Figures In The Coordinate Plane
- topic D: Problem Solving In The Coordinate Plane
- topic E: Multi-Step Word Problems
- topic F: The Years In Review: A Reflection On A Story Of Units
Related Guides and Multimedia
Our professional learning resources include teaching guides, videos, and podcasts that build educators' knowledge of content related to the standards and their application in the classroom.
Number & Operations in Base Ten: Unbound A Guide to Grade 5 Mathematics Standards
- See All Guides
2020 AMC 10A Problems/Problem 23
- 2 Solution 1
- 3 Solution 2 (Rewording of Solution 1)
- 4 Solution 3 (Group Theory)
- 5 Video Solution by Brain Math Club
- 6 Video Solution by Education, The Study of Everything
- 7 Video Solution by Richard Rusczyk
- 8 Video Solution by MathEx
Solution 2 (Rewording of Solution 1)
Solution 3 (Group Theory)
Video Solution by Brain Math Club
https://youtu.be/yAkj_5YMhhQ
Video Solution by Education, The Study of Everything
https://youtu.be/SBhkM2frTUA
Video Solution by Richard Rusczyk
https://artofproblemsolving.com/videos/amc/2020amc10a/513
Video Solution by MathEx
https://www.youtube.com/watch?v=iXwvTmFvo0c
| ( • • ) | ||
| Preceded by | Followed by | |
| ( • • ) | |
| Preceded by | Followed by |
- Introductory Geometry Problems
Something appears to not have loaded correctly.
Click to refresh .
- Math Forum/Help
- Problem Solver
- College Math
- The Coordinate Plane
The Coordinate Plane: Very Difficult Problems with Solutions
If you're seeing this message, it means we're having trouble loading external resources on our website.
If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.
To log in and use all the features of Khan Academy, please enable JavaScript in your browser.
Unit 6: Analytic geometry
About this unit.
In analytic geometry, also known as coordinate geometry, we think about geometric objects on the coordinate plane. For example, we can see that opposite sides of a parallelogram are parallel by writing a linear equation for each side and seeing that the slopes are the same.
Distance and midpoints
- Getting ready for analytic geometry (Opens a modal)
- Distance formula (Opens a modal)
- Midpoint formula (Opens a modal)
- Distance formula review (Opens a modal)
- Midpoint formula review (Opens a modal)
- Distance between two points Get 5 of 7 questions to level up!
- Midpoint formula Get 3 of 4 questions to level up!
Dividing line segments
- Dividing line segments: graphical (Opens a modal)
- Dividing line segments (Opens a modal)
- Proving triangle medians intersect at a point (Opens a modal)
- Divide line segments Get 3 of 4 questions to level up!
Problem solving with distance on the coordinate plane
- Area of trapezoid on the coordinate plane (Opens a modal)
- Points inside/outside/on a circle (Opens a modal)
- Challenge problem: Points on two circles (Opens a modal)
- Coordinate plane word problem (Opens a modal)
- Area & perimeter on the coordinate plane Get 3 of 4 questions to level up!
- Points inside/outside/on a circle Get 3 of 4 questions to level up!
- Coordinate plane word problems: polygons Get 3 of 4 questions to level up!
Parallel & perpendicular lines on the coordinate plane
- Parallel & perpendicular lines intro (Opens a modal)
- Parallel & perpendicular lines from graph (Opens a modal)
- Classifying quadrilaterals on the coordinate plane (Opens a modal)
- Classifying figures with coordinates (Opens a modal)
- Parallel & perpendicular lines from graph Get 3 of 4 questions to level up!
- Classify figures by coordinates Get 3 of 4 questions to level up!
Equations of parallel & perpendicular lines
- Parallel lines from equation (Opens a modal)
- Parallel lines from equation (example 2) (Opens a modal)
- Parallel lines from equation (example 3) (Opens a modal)
- Perpendicular lines from equation (Opens a modal)
- Writing equations of perpendicular lines (Opens a modal)
- Writing equations of perpendicular lines (example 2) (Opens a modal)
- Proof: parallel lines have the same slope (Opens a modal)
- Proof: perpendicular lines have opposite reciprocal slopes (Opens a modal)
- Analytic geometry FAQ (Opens a modal)
- Parallel & perpendicular lines from equation Get 3 of 4 questions to level up!
- Write equations of parallel & perpendicular lines Get 3 of 4 questions to level up!
IMAGES
VIDEO
COMMENTS
"In this module, students develop a coordinate system for the first quadrant of the coordinate plane and use it to solve problems. Students use the familiar number line as an introduction to the idea of a coordinate and construct two perpendicular number lines to create a coordinate system on the plane. They see that just as points on the line can be located by their distance from 0, the plane ...
In geometry, coordinates say where points are on a grid we call the "coordinate plane". We use coordinates to describe where something is. ... Problem solving in all quadrants ... Distance between points: vertical or horizontal Get 5 of 7 questions to level up! Coordinate plane problems in all four quadrants Get 5 of 7 questions to level up ...
How to solve problems related to the distance between points that lie on the same horizontal or vertical line and the coordinate plane, examples with step by step solutions, use the coordinate plane to graph points, line segments and geometric shapes in the various quadrants and then use the absolute value to find the related distances, Common Core Grade 6
Free coordinate plane math topic guide, including step-by-step examples, free practice questions, teaching tips, and more! ... To make the repeated practice more engaging, give students the opportunity to create and use a coordinate plane to solve a real world problem. It could be physical, for example, using string and stakes to create a grid ...
Identify your areas for growth in these lessons: Coordinate plane: quadrant 1. Coordinate plane: 4 quadrants. Quadrants on the coordinate plane. Reflecting points on coordinate plane. Start quiz.
The Coordinate Plane: Problems with Solutions. The x-axis is . The y-axis is . How many coordinates does any point in a plane have? The first coordinate of the point is called . The second coordinate of the point is . The x coordinate of a point in a plane represents .
The plane determined by a horizontal number line, called the x-axis, and a vertical number line, called the y-axis, intersecting at a point called the origin. Each point in the coordinate plane can be specified by an ordered pair of numbers, (x,y). The cordinate system is organized to 4 quadrants. In the first quadrant, both (x,y) are positive.
The idea of coordinate geometry is often credited to Rene Descartes, and the most commonly used coordinate system is often refered to as a Cartesian coordinate system, as a result. Coordinate bashing is applying coordinates to geometry problems. There are two parts of the Cartesian plane: the x-coordinate and the y-coordinate. Sample Problems
In This Module. topic A: Coordinate Systems. topic B: Patterns In The Coordinate Plane And Graphing Number Patterns From Rules. topic C: Drawing Figures In The Coordinate Plane. topic D: Problem Solving In The Coordinate Plane. topic E: Multi-Step Word Problems. topic F: The Years In Review: A Reflection On A Story Of Units.
Graph and solve real-world problems using a coordinate planeIn this lesson you will learn to graph and solve real-world problems by using a coordinate plane....
Problem. Let be the triangle in the coordinate plane with vertices and Consider the following five isometries (rigid transformations) of the plane: rotations of and counterclockwise around the origin, reflection across the -axis, and reflection across the -axis.How many of the sequences of three of these transformations (not necessarily distinct) will return to its original position?
Coordinate plane word problems: polygons. Math > High school geometry > Analytic geometry > Problem solving with distance on the coordinate plane ... Lesson 3: Problem solving with distance on the coordinate plane. Area of trapezoid on the coordinate plane. Area & perimeter on the coordinate plane.
Problem solving in the coordinate plane is the focus of Topic D. Students draw symmetric figures using both angle size and distance from a given line of symmetry. Line graphs are also used to explore patterns and make predictions based on those patterns. To round out the topic, students use coordinate planes to solve real world problems.
Here we use the coordinate plane to find distances of real world problems.
Normal. Difficult. The Coordinate Plane: Difficult Problems with Solutions. By Catalin David. Problem 1. If point A with the coordinates (2, a) is situated on the x-axis, then a = 1 -1 0 2. Solution: If point A is on the x-axis, the distance from A to the x-axis is 0, so a = 0. Problem 2. If point B with the coordinates (a, 3) is situated on ...
Lesson 2: Construct a coordinate system on a plane. Lesson 2 Problem Set 5•6 Name Date 1. a. Use a set square to draw a line perpendicular to the T-axes through points 2, 3, and 4. Label the new line as the U-axis. b. Choose one of the sets of perpendicular lines above and create a coordinate plane. Mark 7 units on
Problem 2. What are the coordinates of M, found halfway between A and B? (3, 4.5) (4.5, 3) (6, 3) Problem 3. Square OCAB has an area of 9 square units. Point O is found where the axes meet.
In analytic geometry, also known as coordinate geometry, we think about geometric objects on the coordinate plane. For example, we can see that opposite sides of a parallelogram are parallel by writing a linear equation for each side and seeing that the slopes are the same. ... Problem solving with distance on the coordinate plane. Start quiz ...
Problem Solving with the Coordinate Plane. Eureka Essentials: Grade 5. An outline of learning goals, key ideas, pacing suggestions, and more! Fluency Games. Downloadable Resources. Teacher editions, student materials, application problems, sprints, etc. Application Problems.
This video applies the distance formula to polygons on a coordinate plane. We find area and perimeter on the plane to compare lengths and area.
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.
In analytic geometry, also known as coordinate geometry, we think about geometric objects on the coordinate plane. For example, we can see that opposite sides of a parallelogram are parallel by writing a linear equation for each side and seeing that the slopes are the same. ... Problem solving with distance on the coordinate plane. Learn. Area ...
Correlates to page 69 of the Spectrum Math Workbook, Grade 6.