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Chapter 3: Problem 41

In which quadrant or on which axis is each point located? $$ (7,-2) $$

Short Answer

Expert verified
Quadrant IV

Step by step solution

01

Identify the coordinates

The given point is (7, -2) In this format, the first number represents the x-coordinate and the second number represents the y-coordinate.
02

Determine the sign of each coordinate

Look at the signs of the coordinates: The x-coordinate (7) is positive, and the y-coordinate (-2) is negative.
03

Locate the quadrant

In the Cartesian plane: 1. Quadrant I has both coordinates positive. 2. Quadrant II has a negative x-coordinate and a positive y-coordinate. 3. Quadrant III has both coordinates negative. 4. Quadrant IV has a positive x-coordinate and a negative y-coordinate. Since the x-coordinate is positive and the y-coordinate is negative, the point (7, -2) is located in Quadrant IV.

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Key Concepts

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

coordinate system
A coordinate system, also known as the Cartesian coordinate system, is used to define the position of points in a plane using ordered pairs of numbers. Each point is represented by two values: an x-coordinate and a y-coordinate. The x-coordinate indicates the horizontal position, while the y-coordinate indicates the vertical position. The system is named after the French mathematician Ren茅 Descartes, who introduced this concept.
positive and negative coordinates
Coordinates can be either positive or negative, depending on their position relative to the origin, which is the point (0,0) where the x-axis and y-axis intersect.
  • Positive x-coordinates are on the right side of the origin.
  • Negative x-coordinates are on the left side.
  • Positive y-coordinates are above the origin.
  • Negative y-coordinates are below the origin.
Understanding the signs of the coordinates helps in determining the location of points in the Cartesian plane.
Cartesian plane quadrants
The Cartesian plane is divided into four regions called quadrants. Each quadrant has a specific combination of positive and negative coordinates:
  • Quadrant I: Both x and y coordinates are positive.
  • Quadrant II: x-coordinates are negative, but y-coordinates are positive.
  • Quadrant III: Both x and y coordinates are negative.
  • Quadrant IV: x-coordinates are positive, but y-coordinates are negative.
For example, the point (7, -2) has a positive x-coordinate (7) and a negative y-coordinate (-2), placing it in Quadrant IV. Knowing this helps in graphing points accurately and solving problems related to the coordinate system.

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