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Chapter 2: Problem 24

In which quadrant or on which axis is each point located? \((7.5,2.9)\)

Short Answer

Expert verified
First quadrant.

Step by step solution

01

Identify the Coordinates

Examine the given point \(7.5, 2.9\). The first number (7.5) is the x-coordinate, and the second number (2.9) is the y-coordinate.
02

Determine the Sign of Each Coordinate

Check the sign of each coordinate. If both coordinates are positive, the point is in the first quadrant; if the x-coordinate is negative and the y-coordinate positive, it's in the second quadrant; if both are negative, it's in the third quadrant; if the x-coordinate is positive and the y-coordinate negative, it's in the fourth quadrant.
03

Analyze the Point \(7.5, 2.9\)

Both 7.5 and 2.9 are positive numbers. Therefore, the point \(7.5, 2.9\) is located in the first quadrant.

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Key Concepts

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

Quadrants
In the coordinate plane system, the entire plane is divided into four quadrants. Imagine the plane is split by a vertical line (the y-axis) and a horizontal line (the x-axis). These lines intersect at the center, called the origin \(0,0\).
  • Quadrant I is where both x and y coordinates are positive.
  • Quadrant II is where the x-coordinate is negative and the y-coordinate is positive.
  • Quadrant III has both x and y coordinates negative.
  • Quadrant IV is where the x-coordinate is positive and the y-coordinate is negative.
Identifying which quadrant a point lies in helps understand its location relative to the origin. For example, the point \(7.5, 2.9\) lies in the first quadrant since both coordinates are positive.
Coordinates
Every point in the coordinate plane is represented by coordinates, written as \((x, y)\). The x-coordinate indicates how far left or right a point is from the y-axis. The y-coordinate shows how far up or down a point is from the x-axis.
  • Positive x-coordinates move right from the y-axis.
  • Negative x-coordinates move left from the y-axis.
  • Positive y-coordinates move up from the x-axis.
  • Negative y-coordinates move down from the x-axis.
For instance, in the point \(7.5, 2.9\), 7.5 is the x-coordinate (rightward) and 2.9 is the y-coordinate (upward).
Positive and Negative Signs
Understanding the positive and negative signs of coordinates is crucial. These signs determine the exact quadrant where a point is located.
  • If both x and y are positive, the point is in the first quadrant.
  • If x is negative and y is positive, it's in the second quadrant.
  • If both x and y are negative, it's in the third quadrant.
  • If x is positive and y is negative, it's in the fourth quadrant.
In our exercise, we analyzed the point \(7.5, 2.9\): both coordinates are positive, placing it in the first quadrant. Simple checks of signs can quickly tell you the quadrant a point belongs to.

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