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Chapter 3: Problem 34

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

Short Answer

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

Step by step solution

01

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.
02

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.
03

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.

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Most popular questions from this chapter

Graph equation. \(3 y=9\)

Graph equation. \(5 y=20\)

Will help you prepare for the material covered in the first section of the next chapter. Is \((-4,3)\) a solution of both \(x+2 y=2\) and \(x-2 y=6 ?\)

Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user's manual for your graphing utility that describes how to shade a region. Then use your graphing utility to graph the inequalities in $$y \leq 4 x+4$$

Compare the graphs of \(3 x-2 y>6\) and \(3 x-2 y \leq 6\) Discuss similarities and differences between the graphs.
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