What Is a Coordinate System?

A coordinate system is a grid that is formed by two number lines crossing each other at the point where the number zero appears on both lines. This intersection is called the origin. A coordinate system looks like this:

The coordinate system with a horizontal x-axis and a vertical y-axis

The $x$ -axis is also called the first axis, while the $y$ -axis is called the the second axis.

You will come across coordinate systems both in math at school and in daily life. Coordinate systems are a tool that help you know where things are located.

Think About This

Look at the coordinate system with the positive numbers on the figure. How do you think you read a point in the grid?

The answer is revealed further down on the page.

A point in the grid is called a coordinate. Every coordinate consists of one value from the first axis and one value from the second axis (see figure).

Below, you can see a coordinate system with points.These points are named after letters in the alphabet. This is how you find the coordinates of a point:

Rule

Read the Coordinates of a Point

1.: Put your finger on the point, then drag your finger straight down until you hit the first axis. Write down the number that is now under your finger.
2.: Put your finger back on the point, then drag your finger straight left until you hit the second axis. Write down the number that is now under your finger.
3.: The coordinates should look like this: $(x, y)$ . You have to replace the x with the number you found on the first axis. You have to replace the y with the number you found on the second axis.

A coordinate system with points plotted in

Think About This

Can you read the coordinates of the different points above?

$A = (1, 1)$	$B = (3, 1)$	$C = (2, 3)$
$D = (4, 3)$	$E = (1, 5)$	$F = (3, 10)$
$G = (8, 7)$	$H = (5, 7)$	$I = (7, 4)$
$J = (7, 7)$	$K = (0, 4)$	$L = (6, 0)$

$A = (1, 1)$	$B = (3, 1)$	$C = (2, 3)$	$D = (4, 3)$
$E = (1, 5)$	$F = (3, 10)$	$G = (8, 7)$	$H = (5, 7)$
$I = (7, 4)$	$J = (7, 7)$	$K = (0, 4)$	$L = (6, 0)$

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What Is the Definition of a Function?

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