6.1The Cartesian Coordinate System

Two number lines at right angles, sharing a common zero, make the Cartesian plane: the horizontal $x$ -axis and the vertical $y$ -axis, crossing at the origin $O(0, 0)$ . Any point is an ordered pair $(x, y)$ , with $x$ measured right or left of the origin and $y$ measured up or down.

The Cartesian plane: points

A(2, 3)

and

B(-3, 1)

, each measured from the origin

O

The $x$ -coordinate is the distance right (positive) or left (negative) of the origin.
The $y$ -coordinate is the distance up (positive) or down (negative).
The origin $O(0, 0)$ is where the two axes cross: zero across, zero up.
A point on the $y$ -axis has $x = 0$ ; a point on the $x$ -axis has $y = 0$ .

Writing coordinates from a description

A point $\displaystyle K$ is 4 units to the right of the $\displaystyle y$ -axis and 6 units below the $\displaystyle x$ -axis. Write down the coordinates of $\displaystyle K$ .

Show solution▾

4 units to the right means

x = 4

6 units below means

y = -6

Coordinates:

K(4, -6)

Now you try

Write down the coordinates of point $A$ .

Show solution▾

A

is 6 units to the right of the origin, so the

x

-coordinate is

6

It is 1 unit up from the

x

-axis, so the

y

-coordinate is

1

A(6, 1)

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