Cartesian Coordinates

Cartesian coordinates are a system for representing points in a plane using two perpendicular axes, typically labeled x and y. This system was developed by René Descartes and provides a way to precisely locate points in a two-dimensional space.

The Coordinate Plane

The coordinate plane consists of two perpendicular number lines, the x-axis and the y-axis. The point where the two axes intersect is called the origin, and is represented by the coordinates (0, 0).

The x-axis is the horizontal axis, with positive values to the right of the origin and negative values to the left. The y-axis is the vertical axis, with positive values above the origin and negative values below.

Coordinates of a Point

To represent a point in the coordinate plane, we use an ordered pair of numbers (x, y), where x is the distance from the y-axis (positive to the right, negative to the left) and y is the distance from the x-axis (positive above, negative below).

Plotting Points

To plot a point on the coordinate plane, start at the origin and move horizontally (left or right) the number of units given by the x-coordinate, then move vertically (up or down) the number of units given by the y-coordinate. The point where you end up is the location of the plotted point.

Study Guide

1. What are Cartesian coordinates?
2. What are the two perpendicular axes in the coordinate plane?
3. What is the origin in the coordinate plane?
4. How do you represent a point in the coordinate plane?
5. How do you plot a point on the coordinate plane?

After studying this topic, you should be able to understand how to represent and locate points in a two-dimensional space using Cartesian coordinates. Practice plotting points and identifying coordinates to strengthen your understanding of this concept.