Cartesian coordinate system

Definition

A Cartesian coordinate system is a two-dimensional plane defined by a horizontal axis (x-axis) and a vertical axis (y-axis). Points on the plane are specified by ordered pairs (x, y).

5 Must Know Facts For Your Next Test

1. The point where the x-axis and y-axis intersect is called the origin, denoted as (0, 0).
2. The x-coordinate indicates horizontal position, while the y-coordinate indicates vertical position.
3. Quadrants are numbered counterclockwise starting from the upper right: I, II, III, IV.
4. A positive slope of a line indicates it rises from left to right; a negative slope indicates it falls.
5. The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) can be found using the distance formula: $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

Review Questions

• What are the coordinates of the origin in a Cartesian coordinate system?
• How do you determine which quadrant a point \((x,y)\) lies in?
• What does it mean for a line to have a positive or negative slope in this system?

Related terms

Slope: The measure of the steepness of a line, calculated as rise over run or $\frac{y_2 - y_1}{x_2 - x_1}$.

Quadrant: One of four regions into which the Cartesian plane is divided by its axes.

Origin: The point of intersection of the x and y axes in a Cartesian coordinate system, designated as (0,0).