Coordinate Plane
A coordinate plane is a grid with a horizontal x-axis and a vertical y-axis crossing at the origin, so every point has an (x, y) address. Choose four quadrants or the first only, the range of the axes, the grid spacing and how many planes to put on the page, and the sheet is drawn for you.
Your sheet
Printing: choose Actual size or 100%, not “Fit to page”, so 1 cm prints as 1 cm. How to check.
How is the plane laid out?
Four quadrants: the axes cross at the centre and each runs from −range to +range, so there are 2 × range ÷ grid squares each way. First quadrant: the axes meet at the bottom-left corner and run from 0 to range.
Worked example. Four quadrants with a range of 10 and a grid of 1 is 20 squares each way. On A4 portrait the plane is 178 mm square, so each square is 8.9 mm. The point (3, −4) is 3 squares right of the origin and 4 squares down, in quadrant IV. Two planes side by side come out at about 79 mm each, and four planes, two across and two down, are the same size, because the width sets the limit.
Plotting points
Read the x-coordinate first and move along the x-axis, then move up or down by the y-coordinate. “Along the corridor, then up the stairs” is the usual reminder. The origin is (0, 0); points on the x-axis have y = 0; points on the y-axis have x = 0.
The four quadrants
Numbered anticlockwise with Roman numerals from the top right: I has both coordinates positive, II has x negative and y positive, III has both negative, IV has x positive and y negative. Knowing the quadrant is a quick check that a plotted point is in the right place.
Graphing lines and shapes
For y = 2x + 1, make a small table of x and y values, plot three points and rule through them. For reflections and translations, plot the shape, apply the rule to each corner and plot again; four planes on one page give one per transformation. For plotting data from an experiment, the graph paper with its own scale often works better.
Questions about the coordinate plane
What is a coordinate plane?
Two number lines at right angles, the x-axis across and the y-axis up, crossing at the origin (0, 0). Any point is named by two numbers, (x, y): how far across, then how far up. The grid behind the axes makes the counting easy.
When do I need all four quadrants?
As soon as negative coordinates appear, usually around age 11 or 12. Before that, the first quadrant (both coordinates positive) is enough and gives bigger squares for the same paper.
What range should the axes run to?
10 is the default and suits most textbook exercises. Use 5 for young children and large handwriting, 12 or 15 when a question needs it, and 20 or more only in landscape or on A3.
Can I put several planes on a page?
Yes: one, two or four. Four small planes on one sheet are ideal for a set of transformation questions, one plane per question.
Why number every other grid line?
With a range of 20 the labels would overlap, so set “Number every” to 2 or 5. The grid lines stay, only the numbers thin out.