Problem 3 In which quadrant is each point ... [FREE SOLUTION]

Chapter 15: Problem 3

In which quadrant is each point located? \((2,1)\)

Short Answer

Expert verified

Quadrant I

Step by step solution

- Understanding the Cartesian Plane

The Cartesian 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, and Quadrant IV is where x is positive and y is negative.

- Identify the Coordinates

Identify the given coordinates which are (2,1). In this case, x = 2 and y = 1.

- Determine the Quadrant

Since both x and y coordinates are positive (x > 0 and y > 0), the point (2,1) lies in Quadrant I.

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Key Concepts

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

Cartesian coordinates

The Cartesian coordinate system is a two-dimensional plane for graphing points, lines, and curves. It consists of two perpendicular lines:
The x-axis (horizontal) and the y-axis (vertical).
These axes intersect at a point called the origin, labeled as \((0,0)\). Each point on the plane is represented by an ordered pair \((x,y)\), where 'x' tells you how far to move horizontally, and 'y' tells you how far to move vertically.
This system makes it easy to locate and plot points precisely. Understanding Cartesian coordinates forms the foundation for many mathematical and scientific concepts.

quadrant identification

The Cartesian plane is divided into four regions called quadrants. These quadrants are labeled counterclockwise starting from the upper right:

Quadrant I: Both x and y are positive \(x > 0, y > 0\).
Quadrant II: x is negative, and y is positive \(x < 0, y > 0\).
Quadrant III: Both x and y are negative \(x < 0, y < 0\).
Quadrant IV: x is positive, and y is negative \(x > 0, y < 0\).

To determine which quadrant a point falls into, simply examine the signs of its x and y coordinates. For example, given the point \((2,1)\), since both x and y are positive, this point lies in Quadrant I.

algebra basics

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. Basic algebra involves operations like addition, subtraction, multiplication, and division using variables instead of numbers. Here are some key concepts:

Variables: Symbols (often letters) that represent numbers or values.
Equations: Mathematical statements that assert the equality of two expressions.
Simplifying: The process of rewriting an expression in a simpler form.

In the context of Cartesian coordinates and quadrant identification, algebra allows us to represent and manipulate the coordinates of points.
This makes it easier to solve problems involving points and lines on the Cartesian plane.

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91影视

In which quadrant is each point located? \((2,1)\)

Short Answer

Step by step solution

- Understanding the Cartesian Plane

- Identify the Coordinates

- Determine the Quadrant

Key Concepts

Cartesian coordinates

quadrant identification

algebra basics

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