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Coordinate plane

Type points or tap the grid, join them into a shape, then print the plane or a sheet of blank ones.

Printable chart
INTERACTIVE AND PRINTABLE

Coordinate plane

xy−10−10−9−9−8−8−7−7−6−6−5−5−4−4−3−3−2−2−1−111223344556677889910100ABCD

Or tap the grid to add a point at the nearest whole numbers.

  1. A(2, 3): from the origin go 2 right, then 3 up. It's in quadrant I.
  2. B(−4, 1): from the origin go 4 left, then 1 up. It's in quadrant II.
  3. C(−3, −4): from the origin go 3 left, then 4 down. It's in quadrant III.
  4. D(5, −2): from the origin go 5 right, then 2 down. It's in quadrant IV.
xy−10−10−9−9−8−8−7−7−6−6−5−5−4−4−3−3−2−2−1−111223344556677889910100xy−10−10−9−9−8−8−7−7−6−6−5−5−4−4−3−3−2−2−1−111223344556677889910100xy−10−10−9−9−8−8−7−7−6−6−5−5−4−4−3−3−2−2−1−111223344556677889910100xy−10−10−9−9−8−8−7−7−6−6−5−5−4−4−3−3−2−2−1−111223344556677889910100

Coordinate planestringmash.com/coordinate-plane

Plotting points

Type a point as A(2, 3), or leave off the name and the next free letter is used. Negative numbers and halves both work. Tapping the grid adds a point at the nearest whole numbers and writes it into the box, so the box always holds the full list.

Each point gets a line saying how to reach it from the origin, and which quadrant it lands in. Tick Join the points to draw lines between them in the order typed. Close the shape adds the last side back to the first point and works out the area inside.

Print gives this plane with its points, or four blank planes to a page for homework and tests. Download SVG saves the plane as a picture that stays sharp at any size.

Reading a coordinate plane

Two number lines cross at right angles. The horizontal one is the x-axis and the vertical one is the y-axis. The point where they meet is called the origin, and it sits at 0 on both.

A point is written as an ordered pair, (x, y). The first number says how far to go across and the second how far to go up or down, and the order matters: (2, 5) and (5, 2) are different places. The formal names for the two numbers are the abscissa and the ordinate.

The axes split the plane into four quadrants, numbered I to IV in Roman numerals. The numbering goes anticlockwise from the top right. In quadrant I both numbers are positive. Quadrant II has a negative x and a positive y, quadrant III has both negative, and quadrant IV has a positive x with a negative y. A point with a 0 in it lies on an axis, not in any quadrant.

The four quadrants

QuadrantWherexyExample
ITop right++(3, 2)
IITop left−+(−3, 2)
IIIBottom left−−(−3, −2)
IVBottom right+−(3, −2)

When children learn it

In the US Common Core, the coordinate plane arrives in grade 5 with the first quadrant only. Standard 5.G.A.1 describes the axes as a pair of perpendicular number lines meeting at the origin. Standard 5.G.A.2 has children graph points in the first quadrant to solve real problems. The 0 to 10 and 0 to 20 ranges above are for that stage.

Grade 6 opens up all four quadrants. Standard 6.NS.C.6 links the signs in an ordered pair to its quadrant, and notes that two points differing only in sign are reflections of each other across one or both axes. Standard 6.NS.C.8 asks for distances between points that share an x or a y value. Join the points shows those lengths for each side.

Where it comes from

The grid is called Cartesian after René Descartes, who published the idea in 1637 while living in the Netherlands. Pierre de Fermat worked it out independently. Neither of them drew two crossing axes, though. Both used a single axis.

The familiar pair of axes came later, after Frans van Schooten and his students translated Descartes's La Géométrie into Latin in 1649.

Questions

Which number comes first in a coordinate?

The x value, across. Then the y value, up or down.

Which way are the quadrants numbered?

Anticlockwise, starting top right. Quadrant I is top right, II top left, III bottom left and IV bottom right.

What quadrant is (0, 4) in?

None. A point with a zero coordinate sits on an axis. (0, 4) is on the y-axis, and (0, 0) is the origin.

How do you find the distance between two points?

If they share an x or a y value, count the difference in the other one. Otherwise use Pythagoras on the differences: from (1, 1) to (4, 5) is √(3² + 4²) = 5. Join the points does this for every side.

Can I print a blank coordinate plane?

Yes. Set Print to four blank planes and use your browser's print. Pick the range first; first-quadrant grids suit grade 5 and four-quadrant grids suit grade 6 and up.

Sources

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