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Chapter 1: Problem 10

Determine the quadrant(s) in which \((x, y)\) is Iocated so that the condition(s) is (are) satisfied. \(x<0\) and \(y<0\)

Short Answer

Expert verified
The point (x, y) is located in quadrant III (Q3).

Step by step solution

01

Understanding the Cartesian Coordinate System

In the 2-dimensional Cartesian Coordinate System, the x-axis and y-axis divide the plane into four quadrants. Quadrant I (Q1) contains all points with positive x and positive y. Quadrant II (Q2) contains all points with negative x and positive y. Quadrant III (Q3) contains all points with negative x and negative y. Quadrant IV (Q4) contains all points with positive x and negative y.
02

Applying the Given Conditions

Using the conditions \( x < 0 \) and \( y < 0 \), it is required to find the quadrant where both x and y are negative.
03

Determining the Quadrant

According to the conditions given, the x and y coordinates of the point must both be negative. This corresponds to Quadrant III (Q3) of the Cartesian Coordinate System.

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