Coordinate Plane

What is the coordinate plane?

The coordinate plane is a flat grid built from two number lines that cross at a point called the origin, written (0, 0). The horizontal line is the x-axis and the vertical line is the y-axis. Every location on the grid has one exact address — an ordered pair (x, y).

x or y — which comes first?

Always read and write the x-coordinate first, then the y-coordinate: it is (across, then up or down). The x-value tells you how far to move left (negative) or right (positive) from the origin; the y-value tells you how far to move down (negative) or up (positive). So (3, 2) means 3 to the right and 2 up, while (−4, 1) means 4 to the left and 1 up.

The four quadrants

The axes split the plane into four quadrants, numbered counter-clockwise starting at the top right:

• Quadrant I — x positive, y positive (top right).
• Quadrant II — x negative, y positive (top left).
• Quadrant III — x negative, y negative (bottom left).
• Quadrant IV — x positive, y negative (bottom right).

A point that sits on an axis — where x or y is 0 — belongs to no quadrant; it is simply on the x-axis, on the y-axis, or at the origin.

How to use this tool

• Tap or click anywhere on the grid to drop a point on the nearest whole-number (lattice) spot.
• Use the x and y steppers to move the point one unit at a time and hear each new pair.
• Follow the dashed guide lines back to each axis to see exactly how the coordinates are read.
• Switch the range between −5 … 5 and −10 … 10, and leave the trail on to compare recent points.

Why it helps

Hearing "three and two" while watching the guide lines drop to the axes ties the spoken pair to its picture, which is exactly the connection students need before graphing lines, shapes, and functions. Turn the voice on and predict the quadrant before you plot.

Good for

Grade 5 introductions to the coordinate plane through middle- and high-school graphing, geometry, and algebra.