What is the coordinate plane?

The coordinate plane in plain words

The coordinate plane is a flat surface with two number lines on it. The x-axis runs left to right, so it is horizontal. The y-axis runs up and down, so it is vertical. They cross at the origin, (0, 0).

Every location has a name: the ordered pair, two numbers in parentheses with a comma between them, (x, y). The first number is the x-coordinate and the second is the y-coordinate, so x always comes first. Each coordinate moves you along one axis only, and swapping the two numbers names a different point.

A positive x-coordinate means right and a negative one means left. A positive y-coordinate means up and a negative one means down. To plot a pair, start at the origin. Move along the x-axis first, then along the y.

• Quadrant I is upper right, with x and y positive.
• Quadrant II is upper left, with x negative and y positive.
• Quadrant III is lower left, with both coordinates negative.
• Quadrant IV is lower right, with x positive and y negative.

The numbering runs counterclockwise from the upper right. Each step to the next quadrant crosses one axis and flips one sign.

A point on an axis has a zero in one coordinate, so it belongs to no quadrant. The origin, with two zeros, belongs to no quadrant either.

The slip worth naming is writing the coordinates in the opposite order. The point (2, 5) means 2 units right and 5 units up, and plotting it as (5, 2) lands on a different point.

ETS lists identifying points in the xy-coordinate plane among the topics for the Mathematics subtest (5759), and an on-screen four-function calculator is provided on that subtest.

Why a paraeducator uses this in class

A grid worksheet asks a student to plot points, and the skill is not the arithmetic. It is deciding which way to move first: sideways before up or down.

Maps and graphs use the same two axes. A school at (4, 1) and a park at (4, 6) sit on one vertical line, because they share an x-coordinate.

The swapped pair is an error worth watching for. A dot at (5, 2) when the table says (2, 5) is settled by asking: 2 across and 5 up, or the other way around?

Worked example

A class plots temperature readings on a grid, starting at the origin (0, 0). The first point is (2, 5).

1. Read the pair in order: the first number is x and the second is y, so x = 2 and y = 5.
2. Move along the x-axis first. Since x = 2 is positive, move 2 units right.
3. From there move in the y direction. Since y = 5 is positive, move 5 units up.
4. The point is right of the y-axis and above the x-axis, which is quadrant I.

Do the same with (-4, 3): x is negative, so move 4 units left, and y is positive, so move 3 units up. That point is in quadrant II.

Practice questions

Continue learning

• Basic algebra: the variables a coordinate stands for.
• Graphs and charts: reading values off a plotted line or a bar chart.

Try it on a full practice test

Once plotting points feels routine, work through the free ParaPathways practice test.

Our study book covers every skill on both subtests, in English and Spanish.