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Chapter 3: Problem 43

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

Short Answer

Expert verified
The point (-4,-3) is in Quadrant III.

Step by step solution

01

- Understand the Coordinate System

In a Cartesian coordinate system, there are four quadrants. Quadrant I: both x and y are positive. Quadrant II: x is negative, y is positive. Quadrant III: both x and y are negative. Quadrant IV: x is positive, y is negative. Points on the axes are not in any quadrant.
02

- Identify the Coordinates of the Point

The given point is (-4, -3). Here, the x-coordinate is -4 and the y-coordinate is -3.
03

- Determine the Quadrant or Axis

Since both the x-coordinate (-4) and the y-coordinate (-3) are negative, the point (-4, -3) 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.

Quadrants
The Cartesian coordinate system is divided into four quadrants. These quadrants help us determine the location of a point based on its coordinates. named Quadrant I, II, III, and IV.

* **Quadrant I**: Both the x and y values are positive.
* **Quadrant II**: The x value is negative, while the y value is positive.
* **Quadrant III**: Both the x and y values are negative.
* **Quadrant IV**: The x value is positive, but the y value is negative.

If a point lies on one of the coordinate axes (x-axis or y-axis), it is not considered to be in any quadrant. Understanding these quadrants makes it easier to quickly identify the position of any point.
Coordinates
Coordinates are pairs of numbers that define the location of a point on the Cartesian coordinate system. Each pair is written as \( (x, y) \).

* **x-coordinate**: This is the first number in the pair and it represents the horizontal distance from the origin (0,0).
* **y-coordinate**: This is the second number in the pair and it represents the vertical distance from the origin.

For example, in the point (-4, -3), -4 is the x-coordinate and -3 is the y-coordinate. These values tell us how far left or right (x) and how far up or down (y) the point is from the origin.
Negative Values
Negative values in coordinates tell us the direction of the point from the origin.

* **Negative x-values**: A point with a negative x-coordinate lies to the left of the y-axis.
* **Negative y-values**: A point with a negative y-coordinate lies below the x-axis.

In our example (-4, -3), both the x and y values are negative. This means the point is 4 units to the left and 3 units below the origin. Because both coordinates are negative, the point is located in Quadrant III, where both x and y are negative. Understanding how negative values affect the position of points helps us quickly determine their location on the Cartesian coordinate system.

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