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 the y -axis increase in increments of 1.	Here, the x -axis increases in equal steps of 2, and the y -axis increases in increments of 0.5.	Here, the x -axis increases in equal steps of 0.25, and the y -axis increases in increments of 5.

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.

For example,

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.

What is a coordinate plane?

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:

1. Determine the horizontal position of the coordinate (the value of \textbf{x} ).
2. Determine the vertical position of the coordinate (the value of \textbf{y} ).
3. 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).

1. Determine the horizontal position of the coordinate (the value of \textbf{x} ).

The x value is -12, so locate -12 on the x -axis. The scale is 1, so -12 is two gridlines after -10.

2Determine 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.

3Follow 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).

Determine the horizontal position of the coordinate (the value of \textbf{x} ).

The x value is -5, so locate -5 on the x -axis. The scale is 2, so -5 is between -4 and -6.

Determine the vertical position of the coordinate (the value of \textbf{y} ).

The y value is -7, so locate -7 on the y -axis. The scale is 2, so -7 is between -6 and -8.

Follow the gridlines until the two values meet and draw a point.

Following between the gridlines…

This gives us the final solution.

Example 3: plot a coordinate on the x-axis

Plot the coordinate B \, (-2,0).

Determine the horizontal position of the coordinate (the value of \textbf{x} ).

The x value is -2, so locate -2 on the x -axis.

Determine the vertical position of the coordinate (the value of \textbf{y} ).

The y value is 0, so locate 0 on the y -axis.

Follow the gridlines until the two values meet and draw a point.

Following the gridlines…

This gives us the final solution.

Example 4: plot a coordinate on the y-axis

Plot the coordinate C \, (0,0.4).

Determine the horizontal position of the coordinate (the value of \textbf{x} ).

The x value is 0, so locate 0 on the x -axis.

Determine the vertical position of the coordinate (the value of \textbf{y} ).

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.

Follow the gridlines until the two values meet and draw a point.

Following the gridlines…

This gives us the final solution.

Example 5: plotting two coordinates

Plot the coordinates R \left(3,- \, \cfrac{3}{2} \, \right) and Q \left(\cfrac{5}{2},- \, 5 \right).

Determine the horizontal position of the coordinate (the value of \textbf{x} ).

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.

Determine the vertical position of the coordinate (the value of \textbf{y} ).

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.

Follow the gridlines until the two values meet and draw a point.

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).

This gives us the final solution.

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.

Determine the horizontal position of the coordinate (the value of \textbf{x} ).

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.

Determine the vertical position of the coordinate (the value of \textbf{y} ).

The y value of the point D is -3, so locate -3 on the y -axis.

Follow the gridlines until the two values meet and draw a point.

Following the gridlines…

The point D is located here.

Repeat this process for the point E…

Repeating the process for the point F…

This gives us the final solution.

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

The next lessons are

• Types of graphs
• Graphing linear equations
• Rate of change

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