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Chapter 1: Problem 12

Determine the quadrant(s) in which \((x, y)\) is Iocated so that the condition(s) is (are) satisfied. $$y<-5$$

Short Answer

Expert verified
The condition \(y<-5\) is satisfied in Quadrant III and Quadrant IV.

Step by step solution

01

Understand the Cartesian Plane

The Cartesian plane is divided into four quadrants. Quadrant I is where both x and y coordinates are positive. Quadrant II is where the x-coordinate is negative and the y-coordinate is positive. Quadrant III is where both the x and y coordinates are negative. And Quadrant IV is where the x-coordinate is positive and the y-coordinate is negative.
02

Analyze given Condition

Looking at the given condition, \(y<-5\), we see that it must be true for any value of x, meaning that this applies to the whole line where y-value is less than -5 on the Cartesian plane.
03

Find the Suitable Quadrants

As per the Cartesian plane and keeping the condition \(y<-5\) in mind, the point \((x, y)\) would exist in Quadrant III and Quadrant IV because only in these two quadrants can the y-coordinate be negative.

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