Cartesian coordinate system

Definition

A Cartesian coordinate system is a two-dimensional plane defined by an x-axis (horizontal) and a y-axis (vertical), used to graphically represent algebraic equations. Each point in the plane is identified by an ordered pair of coordinates $(x, y)$.

5 Must Know Facts For Your Next Test

1. The origin of the Cartesian coordinate system is the point $(0, 0)$ where the x-axis and y-axis intersect.
2. The x-coordinate indicates horizontal position, while the y-coordinate indicates vertical position.
3. Quadrants are numbered I to IV, starting from the top-right and moving counterclockwise.
4. The distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ can be used to find the distance between two points in this system.
5. The midpoint formula $M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$ finds the midpoint between two points.

Review Questions

• What are the coordinates of the origin in a Cartesian coordinate system?
• How do you determine which quadrant a point lies in?
• What formulas can be used to calculate distance and midpoint between two points?

Related terms

Quadrant:

One of four sections into which a Cartesian plane is divided by its axes.

Distance Formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ calculates the distance between two points in a Cartesian plane.

Midpoint Formula: $M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$ finds the midpoint between two points on a Cartesian plane.