Make your own coordinate plane, coordinate grid or graph paper

The parts of a coordinate plane

A coordinate plane is two number lines crossed at right angles at zero. Every point on it is named by an ordered pair (x, y): how far to go across, then how far to go up or down. That order is fixed, so (2, 5) and (5, 2) are different points.

• The horizontal number line is the x-axis and the vertical one is the y-axis. They cross at the origin, (0, 0).
• The x-coordinate comes first and says how far right (positive) or left (negative) of the origin to go. The y-coordinate comes second: up for positive, down for negative.
• The axes cut the plane into four quadrants, numbered with Roman numerals starting at the upper right and going counterclockwise.
• Quadrant I holds points with x and y both positive, quadrant II has x negative and y positive, quadrant III both negative, and quadrant IV x positive and y negative.
• A point with a zero coordinate, such as (0, 4) or (−3, 0), lies on an axis and belongs to no quadrant.

How to make your own coordinate plane

The plane redraws as you type, and nothing leaves your browser.

• Pick a range under Axes: four quadrants from −10 to 10, −5 to 5 or −20 to 20 by twos, or a first-quadrant grid from 0 to 10, 0 to 20 or 0 to 100 by tens. Or type any smallest value, largest value and step for each axis.
• Set the grid: extra lines between grid lines, a darker line every 5 or 10, numbers every line or every few lines, arrowheads, axis names, quadrant numerals, and dots instead of lines.
• Type points and shapes under Plot, one per line, or click the grid in the Plane view to drop a point on the nearest intersection.
• Choose a transformation to preview its image in orange, with the coordinate rule and the image’s coordinates on the answer key.
• Under Worksheet, keep your own shapes or generate plotting, coordinate-reading or transformation questions; under Page, choose Letter or A4 and one to nine grids per sheet.
• Download the PDF with worksheets first and answer keys after, print it straight away, or save the plane as a PNG or SVG.

Plotting points, segments, polygons and lines

Each line of the Plot box is one figure. Name a point once and use its letter afterwards.

• A(2, 3) plots and labels the point A. (4, −1) on its own plots an unnamed point, and so does a bare 4, −1.
• segment A B joins two points; line A B draws the whole line through them, with arrowheads where it leaves the grid.
• polygon A B C closes the shape and shades it. triangle, quadrilateral, rectangle and parallelogram work as well, and the coordinates can go straight in: triangle P(1, 1) Q(4, 1) R(4, 3).
• Without a keyword, two points make a segment and three or more make a polygon. Decimals such as (2.5, −1) and fractions such as (1/2, 3) are fine.
• To graph a linear equation, plot two of its points as a line. For y = 2x + 1 that is line (0, 1) (1, 3).
• Mistakes are reported by line number, for example a point used before its coordinates are given, so nothing silently disappears.

Reflections, rotations, translations and dilations by coordinates

Each transformation is a rule applied to every vertex. The generator draws the image and prints the rule, so students can check both the picture and the arithmetic.

• Reflection across the x-axis: (x, y) → (x, −y). Across the y-axis: (x, y) → (−x, y).
• Reflection across y = x: (x, y) → (y, x). Across y = −x: (x, y) → (−y, −x).
• Rotation of 90° counterclockwise about the origin: (x, y) → (−y, x). 180°: (x, y) → (−x, −y). 90° clockwise, the same as 270° counterclockwise: (x, y) → (y, −x).
• Translation a units right and b units up: (x, y) → (x + a, y + b), with negative numbers for left and down.
• Dilation by a scale factor k from the origin: (x, y) → (kx, ky). Lengths multiply by k and areas by k².
• Reflections, rotations and translations keep every length and angle; only a dilation changes size. Arrows from each vertex to its image make a translation easy to see.

Coordinate plane activities by grade

In the US Common Core standards the coordinate plane arrives in grade 5 and is used in every grade after it.

• Grade 5, 5.G.A.1 and 5.G.A.2: use perpendicular axes to define a coordinate system and graph points in the first quadrant to solve problems. Print first-quadrant grids from 0 to 10 with the Plot the points worksheet.
• Grade 6, 6.NS.C.6: extend the axes to negative numbers, and see that points whose coordinates differ only in sign are reflections across one or both axes. Plot A(3, 2), then (−3, 2), (3, −2) and (−3, −2).
• Grade 6, 6.NS.C.8 and 6.G.A.3: graph points in all four quadrants, draw polygons from their vertices, and find the length of a side joining points with the same x or the same y.
• Grade 8, 8.G.A.3: describe the effect of dilations, translations, rotations and reflections using coordinates. The Transformations worksheet mixes all four.
• Grade 8, 8.G.B.8: use the Pythagorean theorem to find the distance between two points. Any slanted segment on the grid is the hypotenuse of a right triangle drawn along the grid lines.
• High school: the same grids carry slope, linear equations and coordinate proofs, where squares that stay square matter for every angle and distance.

Coordinate grid worksheets with answer keys

Three worksheet types generate their own questions, so every grid on a page can be different and a fresh set is one click away.

• Plot the points: a list of points under each grid for students to plot and label. The key shows them plotted.
• Name the coordinates: points already plotted for students to read, optionally with the quadrant or axis each lies on. The key gives every answer.
• Transformations: a triangle or quadrilateral with an instruction such as “Rotate triangle ABC 180° about the origin”. The key draws the image, prints the rule and lists the image’s coordinates.
• Generated points sit on grid intersections, at least two squares apart where they fit, away from the edges, and spread over every quadrant the grid has. Letters skip I and O, which read as 1 and 0, and are shuffled so A is not always in the same quadrant.
• Transformation figures are kept compact and, wherever possible, clear of their own image, so neither hides the other.
• Up to nine grids per page and 20 pages per PDF, each with its own questions; “New questions” makes another set.

Choosing the range and scale

• Four quadrants from −10 to 10 is the standard practice grid; −5 to 5 gives bigger squares for younger students.
• Use a first-quadrant grid when every value is positive, as in grade 5 and in most real-world data.
• Count by 2s, 5s or 10s when the numbers are large; label every second or fifth line to keep the axes readable.
• Each grid square is always square, even when the x and y steps differ, so shapes are not stretched and slopes look as steep as they are.
• If a range does not start or end on a whole step, the axis is widened to the next grid line and the tool says so.

Printable graph paper, dot paper and semi-log paper

Switch to Graph paper for a full page of grid at a true, measurable size.

• Square sizes: 1/4 inch (four squares per inch, the usual school graph paper), 1/5 inch, 1/8 inch, 1/2 inch, 1 cm, 5 mm and 2 mm.
• A darker line every 4, 5 or 10 squares makes counting faster; dot paper keeps only the intersections for a lighter page.
• Semi-log paper has a logarithmic horizontal axis of one to six cycles and a linear vertical axis. It is the frequency response graph paper used for Bode plots, and it straightens exponential growth and decay.
• Squares are laid out in whole units and centred on the page; print at 100% and a ruler will confirm the size.

Printing tips

• Print at 100% or “Actual size”, not “Fit to page”, whenever the square size matters.
• The Black grid colour survives photocopying; Ink saver uses light grey lines for everyday practice.
• Two grids per page suit a do-now and an exit ticket; four to nine give a full practice sheet.
• The PDF is vector, so lines stay sharp at any size and the text stays selectable. The SVG opens in Illustrator, Inkscape or PowerPoint for further editing.

A coordinate plane for slides and digital lessons

• Project the Plane view and click to plot points live; click a point again to remove it.
• Export a PNG for Google Slides, Seesaw or a learning platform, where students can drag markers onto the grid.
• The plane is drawn with equal squares and clean labels, so it also works as a figure in notes, tests and handouts.