Cartesian Coordinate System Overview

In which quadrant does the point (-1.5, -2.5) lie?

What are the coordinates of the point where the line y = 2x crosses the y-axis?

What is the slope of the line passing through the points (-4, -3) and (4, -1)?

If a point lies on the y-axis, what can you say about its x-coordinate?

What type of correlation does the equation y = -3x - 2 represent?

For which line do both the x- and y-coordinates have the same sign?

Which quadrant will a line be in if it has a positive slope and both x-intercept and y-intercept are positive?

In which quadrant do the cartesian coordinates (-2, 4) lie?

What type of correlation does the equation y = 1/4x - 2 represent?

If a point lies on the x-axis, what can you say about its y-coordinate?

Which line does NOT pass through the origin?

What is the slope of the line passing through the points (-4, -3) and (4, -1)?

If a line has a negative slope and a positive y-intercept, which quadrant will it be in?

In which quadrant do the cartesian coordinates (-4, -1) lie?

Introduction to Cartesian Coordinate System

The Cartesian Coordinate System is a method of locating points in space using an origin, x- and y-axes, and a unit length.
According to legend, French mathematician Rene Descartes developed the system while observing a fly on the ceiling.

Cartesian Graph

A Cartesian graph is composed of a horizontal line (x-axis) and a vertical line (y-axis) that intersect at the origin.
The axes can be divided and numbered using any unit of measurement.
Points are located on the graph using ordered pairs, where the first number is the x-coordinate and the second number is the y-coordinate.

Locating Points

The x-coordinate indicates the distance from the y-axis along the x-axis, and the y-coordinate indicates the distance from the x-axis along the y-axis.
Points can be located in one of four quadrants: I (above x-axis and to the right of y-axis), II (above x-axis and to the left of y-axis), III (below x-axis and to the left of y-axis), and IV (below x-axis and to the right of y-axis).
Quadrant I has positive x- and y-coordinates, Quadrant II has negative x-coordinates and positive y-coordinates, Quadrant III has negative x- and y-coordinates, and Quadrant IV has positive x-coordinates and negative y-coordinates.

Three or More Dimensions

The Cartesian Coordinate System can be extended to three dimensions by adding a z-axis, which begins at the origin and extends in positive and negative directions perpendicular to the coordinate plane.
The z-axis allows for the indication of height or depth of a 3-dimensional figure.

Graphing Lines

Lines can be graphed using Cartesian coordinates and equations, such as y = 2x, y = -3x -2, and y = 1/4x -2.
Points on the graph can be located and connected to form a straight line.

Learn about the Cartesian Coordinate System, which was developed by French mathematician Rene Descartes in the 17th century. This system uses a set of coordinates, an origin point, and axes to locate objects in a two-dimensional space.