Study Guide: The Coordinate Plane
The Coordinate Plane
A coordinate plane is a two-dimensional number line. The vertical line is called the y-axis and the horizontal line is called the x-axis. These lines are perpendicular (90 degrees) to each other. They intersect (meet) at their zero points. This point is called the origin. The axes divide the plane into four quadrants.
The Completeness Property
The completeness property tells us that every point on the coordinate plane has exactly one location. This implies two things:
- Exactly one point on the plane can be defined by each ordered pair of numbers.
- Exactly one ordered pair defines each point on the plane.
How to plot a point
- Always start at the origin: $(0,0)$
- The first number is the x-coordinate. It tells us the number of horizontal units to count from the origin. Positive numbers are toward the right. Negative numbers are toward the left.
- The second number is the y-coordinate. It tells us the number of vertical units to count from the origin. Positive numbers are toward the top. Negative numbers are toward the bottom.
| Point | Coordinates (x, y) | Quadrant |
|---|---|---|
| A | $(3,−2)$ | IV |
| B | $(−8,5)$ | II |
| C | $(−3,−6)$ | III |
| D | $(0,5)$ | on y-axis |
| E | $(−3\frac{1}{2},0)$ | on x-axis |
René Descartes
The coordinate plane is also called the Cartesian Coordinate System. it was invented by René Descartes, who lived in France from 1596 to 1650 CE. Descartes was one of the world's greatest mathematicians, scientists and philosophers.
Until Descartes, people thought that geometry and algebra were two completely different types of math. Descartes showed the close relationship between these two branches of mathematics. His insight led to many important inventions and technical innovations.
Vocabulary
| Term | Description |
|---|---|
| Coordinate Plane | A coordinate plane is formed when two number lines intersect at right angles, and the point of intersection is at zero on each number line. |
| Axes | The number lines are called axes. |
| x-axis | The horizontal number line is the x-axis. |
| y-axis | The vertical number line is the y-axis. |
| Origin | The point where the two axes meet is the origin. |
| Quadrants | The two axes divide the coordinate plane into four quadrants. |
| Quadrant I | Up and to the right. |
| Quadrant II | Up and to the left. |
| Quadrant III | Down and to the left. |
| Quadrant IV | Down and to the right. |
| Ordered Pair | An ordered pair defines the location of a point on the coordinate plane. |
| Coordinates | The numbers in an ordered pair are the coordinates. |
| x-coordinate | The first number in an ordered pair is the x-coordinate. |
| y-coordinate | The first number in an ordered pair is the y-coordinate. |