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Chapter 15: Problem 6

In which quadrant is each point located? \((-1.7,-5.9)\)

Short Answer

Expert verified
Quadrant III

Step by step solution

01

Understand the Quadrants

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

Determine the Signs

Look at the given coordinates \((-1.7, -5.9)\). Identify the signs of the x and y coordinates. Here, x is -1.7 (negative) and y is -5.9 (negative).
03

Identify the Quadrant

Since both x and y coordinates are negative, the point \((-1.7, -5.9)\) is located in Quadrant III.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Coordinate Plane
The coordinate plane is fundamental in mathematics, providing a way to graphically represent equations and inequalities. It consists of two axes: the horizontal x-axis and the vertical y-axis.
The point where these two axes intersect is called the origin, denoted as \(0,0\). From the origin, the plane extends infinitely in all directions, creating four regions called quadrants.
Quadrants
The coordinate plane is divided into four quadrants, each defined by the signs of the coordinates within them:
  • Quadrant I: Both x and y coordinates are positive (e.g., (3, 2)).
  • Quadrant II: The x coordinate is negative, and the y coordinate is positive (e.g., (-3, 2)).
  • Quadrant III: Both x and y coordinates are negative (e.g., (-3, -2)).
  • Quadrant IV: The x coordinate is positive, and the y coordinate is negative (e.g., (3, -2)).
Given the point \(-1.7, -5.9\), observe that both coordinates are negative. Thus, the point lies in Quadrant III.
Negative Coordinates
A negative coordinate simply means the value is less than zero:
  • Negative x-coordinate: Lies to the left of the y-axis.
  • Negative y-coordinate: Lies below the x-axis.
For the point \(-1.7, -5.9\), \(-1.7\) is left of the y-axis, and \(-5.9\) is below the x-axis.
Recognizing these signs helps determine that the point is located in Quadrant III, where both coordinates must be negative.

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