Axis

Cartesian

Chameleon

Coordinate

Dimension

Estimate

Line

Negative

Ordered Pair

Origin

Plane

Point

Quadrant

Scale

An axis is a line that we use to find or draw points and shapes. If we want to talk about more than one axis, we say "axes."

Here is a picture of two axes in a plane:

A man named René Descartes invented the system that we use to graph points in the plane. (You can see some pictures of René Descartes at the MacTutor Math History Archive.) The word Cartesian means "from Descartes," so people often talk about the Cartesian plane when they are using this system.

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A coordinate is a number that tells you where to find a point. Sometimes you need several coordinates to find exactly where a point is. You can think of a point's coordinates as its address.

Some people talk about "the coordinate plane" to show that you can use coordinates to find every point in the plane.

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The word "dimensional" is an adjective that explains how many dimensions something has. For example, a line is one-dimensional, because a creature that lived on a line could only move forward or backward. A plane is two-dimensional, because a creature living in a plane could move forward or backward and up or down.

Our universe is three-dimensional, because we can move forward or backward, up or down, and side to side. Of course, we can move diagonally or follow a curved path, too. However, these are really combinations of the three basic directions. You can reach any point just moving front or back, up or down, and side to side. Try it!

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Here is a picture of a line. A real line is only one-dimensional, but the picture is bigger, so you can see it more easily.

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An ordered pair is a list of two numbers, where the order of the numbers is important. We write the coordinates of a point as an ordered pair, inside parentheses. Some examples of ordered pairs are (1, 2) and (6, 77).

The origin is the point where all of the axes cross. In the plane, the origin has coordinates (0, 0).

In this picture of a plane, the origin has been marked with a red dot:

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A plane is two-dimensional. It seems flat, like a thin piece of paper. However, unlike pieces of paper, planes have no edges. A bug could crawl along a plane forever without falling off.

Here is a picture of part of a plane. It has been colored green to make it easier to see.

A point is one place in space. Points are really zero-dimensional. Of course, we can't draw something that has no dimensions. When we want to show where a point is, we usually draw a dot, like this: . You can imagine that the real point is in the exact center of the dot.

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The two axes divide the plane into four quarters. These quarters are called quadrants. They are numbered from one to four, starting in the upper right-hand corner and moving counterclockwise.

A chameleon's skin is covered with flat, hard objects. These are also called scales. The word scale has several other meanings. How many can you find?

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