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Chapter 3: Problem 60

Fill in each blank with the word positive or the word negative. The point with coordinates \((x, y)\) is in quadrant II if \(x\) is _____ and \(y\) is _____.

Short Answer

Expert verified
The x-coordinate is 'negative' and the y-coordinate is 'positive'.

Step by step solution

01

Understand quadrants in the coordinate plane

The coordinate plane is divided into four quadrants. Quadrant I contains points where both coordinates are positive \((x > 0, y > 0)\). Quadrant II contains points where the x-coordinate is negative and the y-coordinate is positive \((x < 0, y > 0)\).
02

Identify conditions for Quadrant II

A point lies in Quadrant II if and only if the x-coordinate is negative and the y-coordinate is positive. Therefore, these are the conditions to fill in the blanks.
03

Fill in the blanks

Using the information from Step 2, fill in the blanks: the x-coordinate must be 'negative' and the y-coordinate must be 'positive'.

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Key Concepts

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

Quadrant II
The coordinate plane is divided into four sections known as quadrants. Each quadrant has unique properties distinguishing it from the others.
Quadrant II is the section where the x-coordinate of any point is negative, and the y-coordinate is positive.
This means if you move leftward from the origin (0, 0) and then move upward, you will end up in Quadrant II.
Understanding Quadrant II can help in various mathematical tasks, including graphing equations and plotting points correctly.
x-coordinate
The x-coordinate is the first number in an ordered pair (x, y) that represents a point's horizontal position on the coordinate plane.
It indicates how far left or right the point is from the y-axis (vertical axis).
In Quadrant II, the x-coordinate is always negative because points in this quadrant are to the left of the y-axis.
Examples of x-coordinates in Quadrant II could be -1, -5.5, or -10. Its value influences calculations involving horizontal movement on the plane.
y-coordinate
The y-coordinate is the second number in an ordered pair (x, y) that shows a point's vertical position on the coordinate plane.
It tells us how far up or down the point is from the x-axis (horizontal axis).
In Quadrant II, the y-coordinate is positive because points here lie above the x-axis. For instance, values like 3, 6.7, or 15 all qualify as y-coordinates in Quadrant II.
Understanding the y-coordinate is crucial for graphing functions and analyzing changes in vertical positions.
Negative and Positive Values
In the coordinate plane, the values of x and y can be either negative or positive, and these values determine the point's position.
For Quadrant II, the x-coordinate is negative, reflecting leftward movement from the origin. The y-coordinate is positive, indicating upward movement.
Positive and negative values together locate the point in a specific quadrant, and understanding this helps in plotting graphs and solving equations.
Remember, each coordinate should be considered carefully:
  • Negative x-coordinates signify leftward positions
  • Positive y-coordinates signify upward positions

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