The coordinate plane is a flat grid formed by a horizontal x-axis and a vertical y-axis crossing at the origin, (0, 0). Every point is located by an ordered pair, x first then y, such as (3, −2). The two axes divide the plane into four quadrants, numbered I to IV counterclockwise from the upper right.
In Spanish
plano cartesiano
Also called
Cartesian plane, x-y plane, coordinate grid, rectangular coordinate system
To plot a point, start at the origin, move along the x-axis by the first number, then parallel to the y-axis by the second. The signs tell you the quadrant.
Formal definition and notation
The coordinate plane is a plane with two perpendicular number lines, the axes, that meet at their zero points; that point is the origin. Each point P matches exactly one ordered pair(x, y): x is the signed horizontal distance from the y-axis and y is the signed vertical distance from the x-axis. It is also called the Cartesian plane or the rectangular coordinate system.
Symbol
Read it as
Meaning
(x, y)
the point x comma y
an ordered pair: horizontal coordinate first, vertical second
(0, 0)
the origin
where the axes cross
I, II, III, IV
quadrants one to four
numbered counterclockwise, starting at the upper right
Key facts
Always move left or right first for x, then up or down for y.
The origin is (0, 0). Points on the x-axis have y = 0; points on the y-axis have x = 0.
Flipping the sign of one coordinate reflects the point across an axis: (3, 2) and (3, −2) are mirror images across the x-axis.
Each unit on the grid is the same length, so you can find distances, perimeters and areas by counting or subtracting coordinates.
Graphs of equations, such as lines with a slope, are drawn on the coordinate plane.
Quadrant sign rule
Quadrant sign rule
I (+, +), II (−, +), III (−, −), IV (+, −)
x > 0
the point is right of the y-axis (Quadrant I or IV)
y < 0
the point is below the x-axis (Quadrant III or IV)
x = 0 or y = 0
the point is on an axis, not in any quadrant
For two points on the same horizontal or vertical line, the distance is the absolute value of the difference of the coordinates that change: from (−3, 4) to (5, 4) is |5 − (−3)| = 8.
Try it: plot the points
Interactive
Drag point A or B, or focus one and use the arrow keys. The readout gives the ordered pair, the moves from the origin and the quadrant. Try putting a point on an axis.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
A graph is the set of points that fit a rule, such as the line y = 2x. It is drawn on the coordinate plane.
Quick check: 3 questions
Question 1 of 3
What are the coordinates of the origin?
Show answer and explanation
Answer: C. The origin is where the axes cross, at 0 on both: (0, 0). The other choices are one unit away from it.
Question 2 of 3
Which point is in Quadrant III?
Show answer and explanation
Answer: A. Quadrant III has both coordinates negative, (−, −). (2, −5) and (5, −2) are in Quadrant IV, and (−2, 5) is in Quadrant II.
Question 3 of 3
How do you plot (−3, 4) starting at the origin?
Show answer and explanation
Answer: D. x comes first: move 3 to the left because x is negative, then 4 up because y is positive. The other choices swap the coordinates or ignore a sign.
Coordinate Plane: frequently asked questions
What are the four quadrants?
The axes cut the plane into four regions, numbered counterclockwise from the upper right. Quadrant I has (+, +) points, Quadrant II (−, +), Quadrant III (−, −) and Quadrant IV (+, −). So (−6, 2) is in Quadrant II. Points on the axes, including the origin, belong to no quadrant.
What if a point is on an axis?
Then one coordinate is 0 and the point is in no quadrant. Points on the x-axis look like (4, 0) or (−2, 0): no up or down move. Points on the y-axis look like (0, 5) or (0, −1): no left or right move. The origin (0, 0) is on both axes. Graphs often cross the axes at such points, called intercepts.
How do you find the distance between two points?
If the points share an x- or y-coordinate, subtract the other coordinates and take the absolute value: (2, −1) to (2, 6) is |6 − (−1)| = 7. Otherwise, draw a right triangle and use the Pythagorean theorem, or the distance formula: (0, 0) to (3, 4) is √9 + 16 = 5.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 5.G.A.1, CCSS 6.NS.C.8
Cite this entry
Effortless Math Team. “Coordinate Plane.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/coordinate-plane/
Flashcard
TermCoordinate Planex-axis, y-axis, four quadrants
DefinitionA grid made by a horizontal x-axis and a vertical y-axis meeting at (0, 0). Point (3, −2): right 3, down 2.
Number LineA number line is a straight line with numbers placed at equal distances along it, so every point stands for a number. Zero sits in the middle, positive numbers go to the right and negative numbers to the left. Numbers increase from left to right, so a number line shows order, distance and adding as moving.Number System · Grade 2, Grade 3, Grade 6OriginThe origin is the point where the x-axis and the y-axis cross on the coordinate plane. Its coordinates are (0, 0), and it is labeled O. Every ordered pair tells how far to move from the origin: (4, 3) means 4 units right, then 3 units up.Geometry · Grade 5, Grade 6, Grade 8Ordered PairAn ordered pair is two numbers written to locate a point on the coordinate plane. It is written as (x, y): the x-value comes first, and the y-value comes second. From the origin, move x units across, then y units up or down. The order matters: (2, 5) and (5, 2) are different points.Geometry · Grade 5, Grade 6, Grade 7Y-AxisThe y-axis is the up-and-down number line on the coordinate plane, with positive numbers above the origin and negative numbers below it. It meets the x-axis at the origin, (0, 0). A point’s y-coordinate is read along the y-axis, and every point on the y-axis has x-coordinate 0, like (0, 4).Geometry · Grade 5, Grade 6, Grade 7X-AxisThe x-axis is the horizontal number line on the coordinate plane. It crosses the vertical y-axis at the origin, (0, 0). The x-coordinate of a point tells how far to move along the x-axis, and every point on the x-axis has a y-coordinate of 0, such as (5, 0).Geometry · Grade 5, Grade 6, Grade 7LengthLength is how long something is: the distance from one end of an object to the other. You measure it by counting equal units laid end to end with no gaps or overlaps, such as inches, feet, centimeters or meters. A new pencil is about 7 inches long.Measurement · Grade 1, Grade 2, Grade 3PerimeterPerimeter is the total distance around a two-dimensional shape. To find it, add the lengths of all the sides. A rectangle with sides 5 and 3 has perimeter 5 + 3 + 5 + 3 = 16. Perimeter is a length, so it uses length units such as inches or meters, never square units.Geometry · Grade 3, Grade 4, Grade 5SlopeSlope is a number that measures how steep a line is: the change in y divided by the change in x between any two points on the line, often called rise over run. A positive slope rises from left to right, a negative slope falls, and a horizontal line has slope 0.Algebra · Grade 8, Algebra 1QuadrantA quadrant is one of the four regions that the x-axis and y-axis split the coordinate plane into. They are numbered I, II, III and IV counterclockwise, starting at the top right. The signs of a point’s coordinates tell its quadrant: (+, +) is I, (−, +) is II, (−, −) is III and (+, −) is IV.Geometry · Grade 5, Grade 6, Grade 7DifferenceA difference is the result of subtracting one number from another. In 12 − 7 = 5, the difference is 5. It tells how much bigger one number is than another, or how far apart they are on a number line. “The difference of a and b” means a − b, in that order.Operations · Grade 1, Grade 2, Grade 3SideA side is one of the straight line segments that form the outline of a polygon. Two sides meet at each corner, or vertex. A triangle has 3 sides and a square has 4, and adding the lengths of all the sides gives the perimeter.Geometry · Kindergarten, Grade 1, Grade 2HeightHeight is how tall something is: the distance from its bottom to its top, measured straight up and down. In geometry, the height of a shape is the perpendicular distance from a base to the opposite vertex or side, so it always meets the base at a right angle. Area and volume formulas use it.Measurement · Grade 2, Grade 5, Grade 6SquareA square is a quadrilateral with four equal sides and four right angles. It is a special rectangle and a special rhombus at the same time. For a square with side s, the perimeter is 4s, the area is s2, and each diagonal is s√2.Geometry · Kindergarten, Grade 2, Grade 3NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2GraphA graph is a visual display of numbers, relationships, or data. Graphs help you see patterns, compare values, and understand relationships quickly. In algebra, the graph of an equation is the picture of all its solutions on a coordinate plane; in statistics, bar graphs, line graphs and scatter plots display data.Functions · Grade 5, Grade 6, Grade 7Absolute ValueThe absolute value of a number is its distance from zero on the number line, so it is never negative. It is written with two vertical bars: |−6| = 6 and |6| = 6. A positive number and 0 keep their value; a negative number loses its minus sign.Number System · Grade 6, Grade 7, Grade 8IntegerAn integer is a whole number, its opposite, or zero: the counting numbers, their negatives, and zero. The integers are …, −3, −2, −1, 0, 1, 2, 3, … and go on forever in both directions. Integers have no fractional or decimal part, so 4.5 and 12 are not integers.Number System · Grade 6, Grade 7, Grade 8PointA point is an exact location in space. It has no length, no width and no thickness, so it has no size at all. You draw a point as a dot and name it with a capital letter, such as point A. On a coordinate plane, an ordered pair such as (3, 2) names a point.Geometry · Grade 4, Grade 5, Grade 6TransformationA transformation moves or changes a figure on the coordinate plane. The four common transformations are translations (slides), reflections (flips), rotations (turns) and dilations (resizing). The original figure is the preimage and the result is the image, labeled with primes such as A′. Only a dilation changes the size.Geometry · Grade 7, Grade 8, Algebra 1System of EquationsA system of equations is a set of two or more equations that use the same variables and are solved together. Its solution is the values that make every equation true at the same time. For two linear equations, that is the point where the two lines cross. A system can have one solution, none, or infinitely many.Algebra · Grade 8, Algebra 1