Problem 34 - Introductory Algebra for College Students

Question

In which quadrants are the \(x\) -coordinates negative?

Step-by-Step Solution

Answer

The \(x\)-coordinates are negative in Quadrant II and Quadrant III.

Step 1: Understand the Cartesian Coordinate System

The Cartesian system is a coordinate system that specifies each point uniquely in a plane by a set of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis, and the point where they meet is the origin. The axes divide the plane into four quadrants.

Step 2: Identify the Quadrants

The quadrants are usually numbered from 1 to 4 and are arranged counterclockwise from the positive x-axis. Quadrant I: Both \(x\) and \(y\) are positive. Quadrant II: \(x\) is negative and \(y\) is positive. Quadrant III: Both \(x\) and \(y\) are negative. Quadrant IV: \(x\) is positive and \(y\) is negative.

Step 3: Identify Quadrants with Negative \(x\)-coordinates

By identifying the signs of the \(x\) coordinates in each quadrant, it can be seen that Quadrant II and Quadrant III have negative \(x\)-coordinates.