Problem 36 - Introductory Algebra for College Students

Question

In which quadrants do the \(x\) -coordinates and the \(y\) -coordinates have opposite signs?

Step-by-Step Solution

Answer

The \(x\) -coordinates and the \(y\) -coordinates have opposite signs in the second and fourth quadrants.

Step 1: Understand the Cartesian Coordinate System

In the Cartesian coordinate system, the sign of the coordinates differs in each quadrant. Both \(x\) and \(y\) coordinates are positive in the first quadrant. In the second quadrant, \(x\) is negative and \(y\) is positive. In the third quadrant, both coordinates are negative. Finally, in the fourth quadrant, \(x\) is positive and \(y\) is negative.

Step 2: Identify Quadrants with Opposite Signs

The quadrants where the \(x\) -coordinates and the \(y\) -coordinates have opposite signs are the second and fourth quadrants. In the second quadrant, \(x\) is negative and \(y\) is positive, while in the fourth quadrant, \(x\) is positive and \(y\) is negative.