Problem 19 In which quadrant or on which ax... [FREE SOLUTION]

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Intermediate Algebra : Concepts and Applications

Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

10 Edition

Chapter 2: Problem 19

In which quadrant or on which axis is each point located? $(-4,-3)$

Short Answer

Expert verified

The point $(-4, -3)$ is in the third quadrant.

Step by step solution

Identify the Sign of the Coordinates

Look at the coordinates $(-4, -3)$. The first number $-4$ is the x-coordinate, and the second number $-3$ is the y-coordinate. Notice that both coordinates are negative.

Determine the Quadrant

Since both the x-coordinate and the y-coordinate are negative, the point $(-4, -3)$ is located in the third quadrant. The third quadrant is where both x and y are negative.

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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 a fundamental concept in geometry and is used to precisely locate points in a two-dimensional space. It consists of two perpendicular lines called axes.
The horizontal axis is known as the x-axis and the vertical axis is known as the y-axis. Where these two axes intersect is called the origin, denoted by (0,0).
The coordinate plane is divided into four sections called quadrants. Each quadrant has a specific combination of positive and negative values for coordinates.

negative coordinates

In the coordinate system, negative coordinates indicate points that are either to the left of the origin (for negative x-values) or below the origin (for negative y-values).
Negative coordinates are essential for correctly mapping points in the left and lower sections of the coordinate plane. For example, the point (-4, -3) means that the point is 4 units to the left of the origin and 3 units down from the origin.
This helps to understand that any point with a negative x-coordinate will lie to the left of the y-axis, and any point with a negative y-coordinate will lie below the x-axis.

third quadrant

The third quadrant is one of the four sections of the coordinate plane, specifically where both the x-coordinates and y-coordinates are negative.
This means any point in the third quadrant will have coordinates of the form (-x, -y). It's a crucial area for understanding how negative values interact in geometry.
For instance, the point (-4, -3) lies in the third quadrant because both of its coordinates are negative. Knowing this organizing principle helps in quickly identifying the location of a point based on its coordinates.

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91影视

In which quadrant or on which axis is each point located? \((-4,-3)\)

Short Answer

Step by step solution

Identify the Sign of the Coordinates

Determine the Quadrant

Key Concepts

coordinate plane

negative coordinates

third quadrant

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