Lesson 4: Represent Rational Numbers on the Coordinate Plane

Property

An ordered pair, $(x, y)$, gives the coordinates of a point in a rectangular coordinate system.
The first number is the $x$-coordinate.
The second number is the $y$-coordinate.
The phrase 'ordered pair' means the order is important.
The point $(0, 0)$ is called the origin. It is the point where the $x$-axis and $y$-axis intersect.
The horizontal number line is called the $x$-axis.
The vertical number line is called the $y$-axis.
The $x$-axis and the $y$-axis together form the rectangular coordinate system.

Examples

• To plot the point $(2, 5)$, start at the origin, move 2 units to the right along the $x$-axis, and then 5 units up.

• To plot the point $(-4, 1)$, start at the origin, move 4 units to the left along the $x$-axis, and then 1 unit up.

Property

The axes divide a plane into four regions, called quadrants. The quadrants are identified by Roman numerals, beginning on the upper right and proceeding counterclockwise.

Points on the Axes
Points with a $y$-coordinate equal to 0 are on the $x$-axis, and have coordinates $(a, 0)$.
Points with an $x$-coordinate equal to 0 are on the $y$-axis, and have coordinates $(0, b)$.