Cartesian Coordinates

Cartesian coordinates are a system for representing points in a plane using two numbers, called the x-coordinate and the y-coordinate. This system was developed by René Descartes and has become a fundamental concept in mathematics and geometry.

Representation

Each point in a plane can be represented by an ordered pair of numbers (x, y), where x represents the horizontal position and y represents the vertical position. The point (0, 0) is called the origin and serves as the reference point for the coordinate system.

Quadrants

The plane is divided into four quadrants, labeled I, II, III, and IV, which are formed by the x-axis and y-axis. The signs of the coordinates (x, y) determine in which quadrant a point lies. For example, if x is positive and y is positive, the point lies in quadrant I.

Distance Formula

The distance between two points with coordinates (x1, y1) and (x2, y2) can be calculated using the distance formula:

√((x2 - x1)² + (y2 - y1)²).

Practice Problems

1. Plot the points (3, 4), (-2, 5), and (0, -3) on the Cartesian plane.
2. Which quadrant does the point (-5, -2) lie in?
3. Calculate the distance between the points (1, 2) and (4, 6).

These practice problems will help you reinforce your understanding of Cartesian coordinates and how to work with them. Good luck!