The Coordinate Plane - Math Open Reference

Coordinate Plane

A two-dimensional surface on which points are plotted and located by their x and y coordinates

Try this Drag the point A. As you drag note the two numbers that define its position on the plane. Drag the origin to reposition the axes.

The coordinate plane is a two-dimensional surface on which we can plot points, lines and curves. It has two scales, called the x-axis and y-axis, at right angles to each other. The plural of axis is 'axes' (pronounced "AXE-ease"). Points on the plane are located using two numbers - the x and y coordinates. These are the horizontal and vertical distances of the point from a specific location called the origin.

X axis

The horizontal scale is called the x-axis. As you go to the right on the scale from zero, the values are positive and get larger. As you go to the left from zero, they get more and more negative.

Y axis

The vertical scale is called the y-axis. As you go up from zero the numbers are increasing in a positive direction. As you go down from zero they get more and more negative.

Axis labelling

Along each axis you will see small tic marks with numbers. These are labels to help judge the scale. They are shown every 5 units in the figure above, but can be any increment, and need not be the same on both axes.

Origin

The point where the two axes cross (at zero on both scales) is called the origin. The origin is the point from which all distances along the x and y axes are measured. In the figure above you can drag the origin point to reposition it to a more suitable location at any time.

Quadrants

Quadrants of the coordinate plane The two axes divide the plane into four areas called quadrants. The first quadrant, by convention, is the top right, and then they go around counter-clockwise. In the diagram above they are labelled Quadrant 1,2 etc. It is conventional to label them with numerals but we talk about them as "first, second, third, and fourth quadrant". They are also sometimes labelled with Roman numerals: I, II, III and IV.

In the diagram above, you can drag the origin all the way into any corner and display just one quadrant at a time if you wish.

Things to try

In the figure at the top of the page, first press 'reset'.

Drag the origin point around, including dragging it all the way into a corner to show only one quadrant.
Drag the point A into each quadrant. The first number after the A is the x-coordinate and the second the y-coordinate. Note how the signs of each change in each quadrant. For more on this see Coordinates of a Point